arXiv subjects

Hidekazu Yoshioka

Publications and source records attributed to Hidekazu Yoshioka.

At least 37 records · Page 2Linked to original sources

arXiv2025

Non-Markovian superposition process model for stochastically describing concentration-discharge relationship

Concentration-discharge relationship is crucial in river hydrology, as it reflects water quality dynamics across both low- and high-flow regimes. However, its mathematical description is still challenging owing to the underlying complex physics and chemistry. This study proposes an infinite-dimensional stochastic differential equation model that effectively describes the concentration-discharge relationship while staying analytically tractable, along with the computational aspects of the model. The proposed model is based on the superposition of the square-root processes (or Cox-Ingersoll-Ross processes) and its variants, through which both the long-term moments and autocovariance of river discharge and the fluctuation of water quality index can be derived in closed forms. Particularly, the model captures both long (power decay) and short (exponential decay) memories of the fluctuation in a unified manner, while quantifying the hysteresis in the concentration-discharge relationship through mutual covariances with time lags. Based on a verified numerical method, the model is computationally applied to weekly data on total nitrogen (TN. long memory with moderate fluctuation), total phosphorus (TP. short memory with large fluctuation), and total organic carbon (TOC. short memory with moderate fluctuation) from a rural catchment to validate its applicability to real-world datasets. Based on the identified model and its mutual covariance, our findings indicate that, on average, the peak concentrations of these water quality indices appear approximately 1 day after discharge. Finally, the study discusses the effects of model uncertainty on mutual covariance.

math.PR↗

arXiv2025

Stochastic volatility model with long memory for water quantity-quality dynamics

Water quantity and quality are vital indices for assessing fluvial environments. These indices are highly variable over time and include sub-exponential memory, where the influences of past events persist over long durations. Moreover, water quantity and quality are interdependent, with the former affecting the latter. However, this relationship has not been thoroughly studied from the perspective of long-memory processes, which this paper aims to address. We propose applying a new stochastic volatility model, a system of infinite-dimensional stochastic differential equations, to describe dynamic asset prices in finance and economics. Although the stochastic volatility model was originally developed for phenomena unrelated to the water environment, its mathematical universality allows for an interdisciplinary reinterpretation: river discharge is analogous to volatility, and water quality to asset prices. Moreover, the model's infinite-dimensional nature enables the analytical description of sub-exponential memory. The moments and autocorrelations of the model are then obtained analytically. We mathematically analyze the stochastic volatility model and investigate its applicability to the dynamics of water quantity and quality. Finally, we apply the model to real time-series data from a river in Japan, demonstrating that it effectively captures both the memory and the correlation of water quality indices to river discharge. This approach, grounded in infinite-dimensional stochastic differential equations, represents a novel contribution to the modelling and analysis of environmental systems where long memory processes play a role.

math.PR↗

arXiv2025

Superposition of interacting stochastic processes with memory and its application to migrating fish counts

Stochastic processes with long memories, known as long memory processes, are ubiquitous in various science and engineering problems. Superposing Markovian stochastic processes generates a non-Markovian long memory process serving as powerful tools in several research fields, including physics, mathematical economics, and environmental engineering. We formulate two novel mathematical models of long memory process based on a superposition of interacting processes driven by jumps. The mutual excitation among the processes to be superposed is assumed to be of the mean field or aggregation form, where the former yields a more analytically tractable model. The statistics of the proposed long memory processes are investigated using their moment-generating function, autocorrelation, and associated generalized Riccati equations. Finally, the proposed models are applied to time series data of migrating fish counts at river observation points. The results of this study suggest that an exponential memory or a long memory model is insufficient; however, a unified method that can cover both is necessary to analyze fish migration, and our model is exactly the case.

math.PR↗

arXiv2025

Generalized replicator dynamics based on mean-field pairwise comparison dynamic

The pairwise comparison dynamic is a forward ordinary differential equation in a Banach space whose solution is a time-dependent probability measure to maximize utility based on a nonlinear and nonlocal protocol. It contains a wide class of evolutionary game models, such as replicator dynamics and its generalization. We present an inverse control approach to obtain a replicator-type pairwise comparison dynamic from the large discount limit of a mean field game (MFG) as a coupled forward-backward system. This methodology provides a new interpretation of replicator-type dynamics as a myopic perception limit of the dynamic programming. The cost function in the MFG is explicitly obtained to derive the generalized replicator dynamics. We present a finite difference method to compute these models such that the conservation and nonnegativity of the probability density and bounds of the value function can be numerically satisfied. We conduct a computational convergence study of a large discount limit, focusing on potential games and an energy management problem under several conditions.

math.OC↗

arXiv2024

A mean field Jacobi process for modeling sustainable tourism

A mean field Jacobi process governing the dynamics of the travel demand of agents is formulated and its application to sustainable tourism is investigated both mathematically and computationally. The bounded nature of the Jacobi diffusion process enables the categorization of tourism state with sustainable tourism state corresponding to an internal solution and overtourism state to a boundary solution. A stochastic control framework is introduced to design sustainable tourism under uncertainty, incorporating model distortion conditions owing to misspecification. The control problem is reduced to solving the optimality system of a stationary mean field game whose closed-form solution is derived under certain conditions. The optimality system can be computed numerically using the finite difference method under more general conditions. We present demonstrative examples of the mean field Jacobi process for different parameter values, illustrating both sustainable tourism and overtourism cases. Our findings suggest that the sustainable tourism state cannot be realized if the fluctuation or model misspecification is large.

math.OC↗

arXiv2024

Environmental management and restoration under unified risk and uncertainty using robustified dynamic Orlicz risk

Environmental management and restoration should be designed such that the risk and uncertainty owing to nonlinear stochastic systems can be successfully addressed. We apply the robustified dynamic Orlicz risk to the modeling and analysis of environmental management and restoration to consider both the risk and uncertainty within a unified theory. We focus on the control of a jump-driven hybrid stochastic system that represents macrophyte dynamics. The dynamic programming equation based on the Orlicz risk is first obtained heuristically, from which the associated Hamilton-Jacobi-Bellman (HJB) equation is derived. In the proposed Orlicz risk, the risk aversion of the decision-maker is represented by a power coefficient that resembles a certainty equivalence, whereas the uncertainty aversion is represented by the Kullback-Leibler divergence, in which the risk and uncertainty are handled consistently and separately. The HJB equation includes a new state-dependent discount factor that arises from the uncertainty aversion, which leads to a unique, nonlinear, and nonlocal term. The link between the proposed and classical stochastic control problems is discussed with a focus on control-dependent discount rates. We propose a finite difference method for computing the HJB equation. Finally, the proposed model is applied to an optimal harvesting problem for macrophytes in a brackish lake that contains both growing and drifting populations.

math.OC↗

arXiv2024

Fishery resources management

We consider management of the fish species Plecoglossus altivelis altivelis, a major inland fishery resource in Japan playing important roles from economic, cultural, and recreational viewpoints. We firstly summarize the collected body weight data of the fish in the Hii River, Japan since 2016. The two kinds of data are available in each year with few exceptions: the historical data during summer and autumn collected with the help of an angular and the annual distribution data at the Toami (casting net) competition where we could obtain the data from many anglers during two hours in one day. We fit deterministic and uncertain logistic growth models to the data in each year and discuss their performance. The fitted uncertain logistic growth model is applied to an optimal harvesting problem of the fish subject to a sustainability concern and model distortion. Several numerical schemes for solving the problem are examined and compared both theoretically and numerically.

cs.CE↗

arXiv2024

Computational analysis on a linkage between generalized logit dynamic and discounted mean field game

Logit dynamics are dynamical systems describing transitions and equilibria of actions of interacting players under uncertainty. An uncertainty is embodied in logit dynamic as a softmax type function often called a logit function originating from a maximization problem subjected to an entropic penalization. This study provides another explanation for the generalized logit dynamic, particularly its logit function and player's heterogeneity, based on a discounted mean field game subjected to the costly decision making of a representative player. A large discount limit of the mean field game is argued to yield a logit dynamic. Further, mean field games that lead to classical and generalized logit dynamics are clarified and their well posedness is discussed. Additionally, numerical methods based on a finite difference discretization for computing generalized logit dynamics and corresponding mean field games are presented. Numerical methods are applied to two problems arising in the management of resources and environment; one involves an inland fisheries management problem with legal and illegal anglers, while the other is a sustainable tourism problem. Particularly, cases that possibly lack the regularity condition to be satisfied for the unique existence of stationary solutions are computationally discussed.

math.OC↗

arXiv2024

Generalized pair-wise logit dynamic and its connection to a mean field game: theoretical and computational investigations focusing on resource management

Logit dynamics are evolution equations that describe transitions to equilibria of actions among many players. We formulate a pair-wise logit dynamic in a continuous action space with a generalized exponential function, which we call a generalized pair-wise logit dynamic, depicted by a new evolution equation nonlocal in space. We prove the well-posedness and approximability of the generalized pair-wise logit dynamic to show that it is computationally implementable. We also show that this dynamic has an explicit connection to a mean field game of a controlled pure-jump process, with which the two different mathematical models can be understood in a unified way. Particularly, we show that the generalized pair-wise logit dynamic is derived as a myopic version of the corresponding mean field game, and that the conditions to guarantee the existence of unique solutions are different from each other. The key in this procedure is to find the objective function to be optimized in the mean field game based on the logit function. The monotonicity of the utility is unnecessary for the generalized pair-wise logit dynamic but crucial for the mean field game. Finally, we present applications of the two approaches to fisheries management problems with collected data.

math.OC↗

arXiv2024

Orlicz regrets to consistently bound statistics of random variables with an application to environmental indicators

Evaluating environmental variables that vary stochastically is the principal topic for designing better environmental management and restoration schemes. Both the upper and lower estimates of these variables, such as water quality indices and flood and drought water levels, are important and should be consistently evaluated within a unified mathematical framework. We propose a novel pair of Orlicz regrets to consistently bound the statistics of random variables both from below and above. Here, consistency indicates that the upper and lower bounds are evaluated with common coefficients and parameter values being different from some of the risk measures proposed thus far. Orlicz regrets can flexibly evaluate the statistics of random variables based on their tail behavior. The explicit linkage between Orlicz regrets and divergence risk measures was exploited to better comprehend them. We obtain sufficient conditions to pose the Orlicz regrets as well as divergence risk measures, and further provide gradient descent-type numerical algorithms to compute them. Finally, we apply the proposed mathematical framework to the statistical evaluation of 31-year water quality data as key environmental indicators in a Japanese river environment.

math.ST↗

arXiv2024

A rational logit dynamic for decision-making under uncertainty: well-posedness, vanishing-noise limit, and numerical approximation

The classical logit dynamic on a continuous action space for decision-making un-der uncertainty is generalized to the dynamic where the exponential function for the softmax part has been replaced by a rational one that includes the former as a special case. We call the new dynamic as the rational logit dynamic. The use of the rational logit function implies that the uncertainties have a longer tail than that assumed in the classical one. We show that the rational logit dynamic admits a unique measure-valued solution and the solution can be approximated using a fi-nite difference discretization. We also show that the vanishing-noise limit of the rational logit dynamic exists and is different from the best-response one, demon-strating that influences of the uncertainty tail persist in the rational logit dynamic. We finally apply the rational logit dynamic to a unique fishing competition data that has been recently acquired by the authors.

math.DS↗

arXiv2023

Optimal harvesting policy for biological resources with uncertain heterogeneity for application in fisheries management

Conventional harvesting problems for natural resources often assume physiological homogeneity of the body length/weight among individuals. However, such assumptions generally are not valid in real-world problems, where heterogeneity plays an essential role in the planning of biological resource harvesting. Furthermore, it is difficult to observe heterogeneity directly from the available data. This paper presents a novel optimal control framework for the cost-efficient harvesting of biological resources for application in fisheries management. The heterogeneity is incorporated into the resource dynamics, which is the population dynamics in this case, through a probability density that can be distorted from the reality. Subsequently, the distortion, which is the model uncertainty, is penalized through a divergence, leading to a non-standard dynamic differential game wherein the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation has a unique nonlinear partial differential term. Here, the existence and uniqueness results of the HJBI equation are presented along with an explicit monotone finite difference method. Finally, the proposed optimal control is applied to a harvesting problem with recreationally, economically, and ecologically important fish species using collected field data.

math.OC↗

arXiv2023

Assessing fluctuations of long-memory environmental variables based on the robustified dynamic Orlicz risk

Environmental variables that fluctuate randomly and dynamically over time, such as water quality indices, are considered to be stochastic. They exhibit sub-exponential memory structures that should be accounted for in their modeling and analysis. Furthermore, risk assessments based on these environmental variables should consider limited data availability, which may introduce errors, e.g., model misspecifications, into their modeling. In this study, we present a pair of risk measures to determine the exponential disutility of a generic environmental variable both from below and above. The generic environmental variable is modelled as an infinite-dimensional nonlinear as well as affine stochastic differential equation and its moments and sub-exponential autocorrelations are estimated analytically. Novel risk measures, called dynamic robustified Orlicz risks, are formulated subsequently, and long, sub-exponential memory is efficiently addressed using them. The worst-case upper and lower bounds of the disutility are identified in closed form from the Hamilton-Jacobi-Bellman equations associated with the Orlicz risks. Finally, the proposed methodology is applied to weekly water quality data in a river environment in Japan.

math.OC↗

arXiv2023

Non-singularity of the generalized logit dynamic with an application to fishing tourism

Generalized logit dynamic defines a time-dependent integro-differential equation with which a Nash equilibrium of an iterative game in a bounded and continuous action space is expected to be approximated. We show that the use of the exponential logit function is essential for the approximability, which will not be necessarily satisfied with functions with convex exponential-like functions such as q-exponential ones. We computationally analyze this issue and discuss influences of the choice of the logit function through an application to a fishing tourism problem in Japan.

math.NA↗

arXiv2023

A Jump Ornstein-Uhlenbeck Bridge Based on Energy-optimal Control and Its Self-exciting Extension

We study a version of the Ornstein-Uhlenbeck bridge driven by a spectrally-positive subordinator. Our formulation is based on a Linear-Quadratic control subject to a singular terminal condition. The Ornstein-Uhlenbeck bridge, we develop, is written as a limit of the obtained optimally controlled processes, and is shown to admit an explicit expression. Its extension with self-excitement is also considered. The terminal condition is confirmed to be satisfied by the obtained process both analytically and numerically. The methods are also applied to a streamflow regulation problem using a real-life dataset.

math.OC↗

arXiv2023

Statistical evaluation of a long-memory process using the generalized entropic Value-at-Risk

The modeling and identification of time series data with a long memory are important in various fields. The streamflow discharge is one such example that can be reasonably described as an aggregated stochastic process of randomized affine processes where the probability measure, we call it reversion measure, for the randomization is not directly observable. Accurate identification of the reversion measure is critical because of its omnipresence in the aggregated stochastic process. However, the modeling accuracy is commonly limited by the available real-world data. One approach to this issue is to evaluate the upper and lower bounds of a statistic of interest subject to ambiguity of the reversion measure. Here, we use the Tsallis Value-at-Risk (TsVaR) as a convex risk measure to generalize the widely used entropic Value-at-Risk (EVaR) as a sharp statistical indicator. We demonstrate that the EVaR cannot be used for evaluating key statistics, such as mean and variance, of the streamflow discharge due to the blowup of some exponential integrand. In contrast, the TsVaR avoids this issue because it requires only the existence of some polynomial, not exponential moment. As a demonstration, we apply the semi-implicit gradient descent method to calculate the TsVaR and corresponding Radon-Nikodym derivative for time series data of actual streamflow discharges in mountainous river environments.

stat.ME↗

arXiv2022

Stochastic optimization of a mixed moving average process for controlling non-Markovian streamflow environments

We investigated a cost-constrained static ergodic control problem of the variance of measure-valued affine processes and its application in streamflow management. The controlled system is a jump-driven mixed moving average process that generates realistic subexponential autocorrelation functions, and the static nature of the control originates from a realistic observability assumption in the system. The Markovian lift was effectively used to discretize the system into a finite-dimensional process, which is easier to analyze. The resolution of the problem is based on backward Kolmogorov equations and a quadratic solution ansatz. The control problem has a closed-form solution, and the variance has both strict upper and lower bounds, indicating that the variance cannot take an arbitrary value even when it is subject to a high control cost. The correspondence between the discretized system based on the Markovian lift and the original infinite-dimensional one is discussed. Then, a convergent Markovian lift is presented to approximate the infinite-dimensional system. Finally, the control problem was applied to real cases using available data for a river reach. An extended problem subject to an additional constraint on maintaining the flow variability was also analyzed without significantly degrading the tractability of the proposed framework.

math.OC↗

arXiv2022

A supCBI process with application to streamflow discharge and a model reduction

We propose a new stochastic model for streamflow discharge timeseries as a jump-driven process, called a superposition of continuous-state branching processes with immigration (a supCBI process). It is a non-Markovian model having the capability of reproducing the subexponential autocorrelation found in the hydrological data. The Markovian embedding as a version of matrix analytic methods is applied to the supCBI process, successfully yielding analytical formulae of statistical moments and autocorrelation. The supCBI process is identified at study sites, where hourly streamflow discharge data are available. We also consider another Markovian embedding as a model reduction of the supCBI process to a continuous-time binary semi-Markov chain of high- and low-flow regimes. We show that waiting times can be modeled using a mixture of exponential distributions, suggesting that semi-Markov chains serve as effectively reduced models of the supCBI process.

stat.ME↗