arXiv subjects

Hidekazu Yoshioka

Publications and source records attributed to Hidekazu Yoshioka.

At least 19 recordsLinked to original sources

arXiv2026

Tractable infinite-dimensional model for long-term environmental impact assessment of long-memory deacay processes

Focusing on the assessment of benthic algae blooms that decay subexponentially, we propose a tractable (solvable in a semi-explicit form) and well-defined (that does not diverge) environmental index for the impact assessment of long-memory processes under model uncertainties. Our target system generates long-memory decay through an infinite superposition of multiscale processes. The sensitivity of the environmental index can be controlled by the degree of model uncertainty in terms of the relative entropy and nonexponential discount; hence, we apply a long-memory discount to evaluate long-memory processes. In our framework, the evaluation of the environmental index is reduced to finding a proper solution to an infinite-dimensional extended Hamilton-Jacobi-Bellman system. We solve this system, verify a reasonable solution, and numerically handle it by using a quantization technique. Finally, we present a demonstrative application of the proposed framework to benthic algae population dynamics in river environments based on a laboratory experiment. This paper offers a tractable framework for the assessment of persistent environmental phenomena.

math.OC↗

arXiv2026

Diffusion bridge with randomized initial and terminal times and its application to fish migration

We mathematically model the dynamics of the number of migratory fish observed at a fixed location along a river in a random environment. Particularly, as a new approach, we construct a stochastic differential equation that incorporates the influence of environmental factors on the fluctuations in the start and end of migration. The model is a diffusion bridge with a non-Lipschitz diffusion coefficient, called the Cox-Ingersoll-Ross bridge, and has random initial and terminal times arising from time-change, so that the influences of environmental factors can be efficiently incorporated. The well-posedness of the model is first established, which is considered novel and significant in applied mathematics. Second, we estimate the parameters of the model based on the latest multiyear daily data set for the upstream migration of Plecoglossus altivelis altivelis (Ayu) by relying on the hypothesis that water temperature affects the migration of the fish, which has been suggested in existing studies. We also explore the application of the proposed model to the challenging task of analyzing environmental DNA data. This study advances the development of a theory of fish migration that is simple yet can take environmental factors into account.

q-bio.PE↗

arXiv2026

Stochastic partial differential equation model for environmental DNA dynamics in river environments

Environmental DNA (eDNA) has emerged as a novel tool for quantifying the seasonal abundance of aquatic species in water bodies; however, its mathematical modeling is still at a germinating stage because of its mechanistic uncertainties. We propose a first-step mathematical and computational framework for the eDNA dynamics of migratory fish based on a novel stochastic partial differential equation model with a delayed source input. The model governs spatiotemporal eDNA concentration in rivers where the source comes from a stochastic differential equation for the migration dynamics of the fish. The affine nature of the model facilitates its theoretical analysis, including the guarantee of well-posedness and the closed-form derivation of the Laplace functional despite the proportionality coefficient of the multiplicative noise term being non-Lipschitz. We also propose a discretization scheme for the model that theoretically generates nonnegative numerical solutions. We finally apply the proposed model to eDNA concentration data sampled from midstream reaches of a river system and perform sensitivity analysis.

q-bio.QM↗

arXiv2026

Nonexchangeable logit dynamics with cost constraints: different viewpoints and numerical analysis

The logit dynamic, a nonlinear dynamical system, subject to a const constraint with heterogeneous agents is formulated, and its well-posedness is studied from both agent-based (stochastic differential equation: SDE) and probabilistic (Fokker-Planck equation: FPE) viewpoints. The state space of agent actions is a compact domain in a finite-dimensional Euclidean space. The SDE is of the McKean-Vlasov type and is driven by jumps with finite variations, whereas the FPE is a nonlinear integro-differential equation. A key to our mathematical analysis of the FPE is adding a regularization factor into the cost constraint to mitigate the blow-up of the logit function. This property carries over to the McKean-Vlasov SDE. We also present a numerical method based on a naïve finite difference discretization for computing the FPE along with demonstrative computational examples, showing that the regularization method does not critically affect numerical solutions while preventing the breakdown of numerical computation. Finally, we conduct another demonstrative application study in which environmental, energy, and fishery resources intersect.

math.DS↗

arXiv2026

Forward-looking evolutionary game dynamics subject to exploration cost

We extend classical evolutionary game dynamics based on the momentary action choices of agents by accounting for two elements: forward-looking behavior and exploration cost. We focus on pairwise comparison protocols that cover major evolutionary game dynamics, such as replicator and logit models. In the proposed mathematical framework, agents update their actions by paying a cost so that a utility or its relative difference is maximized. We show that forward-looking behavior can be modeled as a coupling between the evolutionary game dynamic and static Hamilton-Jacobi-Bellman equation: a mean field game. The exploration cost and its constraint are naturally related to these equations as a function of the optimal Lagrangian multiplier serving as a relaxation parameter, and it is incorporated into the game as a constraint. We show that under certain conditions, our evolutionary game dynamic admits a unique solution. Finally, we computationally investigate one- and two-dimensional problems.

math.OC↗

arXiv2026

Diffusion bridge with misspecification: theory construction and application to high-resolution fish count data

Stochastic processes of bridge types having pinned initial and terminal conditions have been widely used in applied research areas, but they all have a common drawback in that the model at hand is possibly misspecified owing to its stochastic nature; namely, parameter values and coefficients are distorted compared to the ground truth. We consider a pair of novel exactly-solvable optimization problems that provide both the lower and upper bounds of the performance index of a diffusion bridge. Our formulation is based on the Girsanov transformation, in which the model uncertainty is measured through relative entropy. We provide a sufficient condition under which these optimization problems are well-posed, and hence admit the corresponding maximizer/minimizer that achieves the worst-case lower and upper bounds given the ambiguity aversion or uncertainty size. We apply the proposed method to the latest 10-min, high-resolution fish count data of a migratory fish in a river and discuss the influence of model uncertainty on the estimation of the total fish count, which is an important problem in resource and environmental management.

math.PR↗

arXiv2026

Distributionally robust decision-making under ambiguity: case study of water environmental management

Decision-making under uncertainty is ubiquitous in environmental project planning. Environmental processes such as a streamflow discharge often present a subexponential memory, where the autocorrelation persists for a long time. In addition, optimization problems driven by environmental processes encounter the issue of model ambiguity because of a lack of sufficient data for model identification. To facilitate decision-making for the management of aquatic environments (e.g., flood mitigation, water abstraction for hydropower generation), we formulate a unified distributionally robust stochastic optimization problem based on a mixed moving average (MMA) process. The MMA process is a superposition of infinite-dimensional affine stochastic processes that is seemingly complex, but the affine property helps with the formulation and computation of the optimization. Our problem is based on a convex objective with a nonsmooth conditional value-at-risk measure. We present a convergent regularization to obtain its smooth and strictly convex counterpart. The model ambiguity is represented as a distortion of the probability density of the target dynamics, and it is penalized by a divergence with which the optimization problem remains convex and becomes computable. As a case study, we apply the optimization problem to two cases with identified parameter values. The performance of the optimized dynamics is evaluated through a statistical simulation. This paper serves as a multidisciplinary work covering both the theory and application of distributionally robust optimization.

math.OC↗

arXiv2026

Mathematical model for sustainable fisheries resource management accounting for size spectrum

This paper proposes a novel modelling and control framework for growth models that incorporate a size spectrum in conjunction with numerical computation and extensive field surveys. In fisheries management, the size spectrum, characterized by individual differences in body weight and length, is a critical factor, as it influences the physiology and ecology of fish, as well as the preferences of anglers. However, a comprehensive theoretical framework for fisheries modelling and management that accounts for the size spectrum has yet to be established. We apply a growth model that considers the size spectrum to Plecoglossus altivelis altivelis (Ayu), an important inland fisheries resource in Japan. Additionally, we introduce a novel stochastic control theory for the resource management of Ayu, taking its size spectrum into account. The growth model is calibrated using data collected annually from a river system in Japan. Our control problem addresses the size spectrum of fishing benefits and terminal utility (nonlinear expectation) for sustainability, resulting in a nonstandard problem to which the dynamic programming principle does not apply. We address this difficulty using a time-inconsistent formalism, where solving the control problem is reduced to finding an appropriate solution to a system of nonlinear partial differential equations. We numerically compute the system using the finite difference method and explore the fisheries management of Ayu at the study site.

math.OC↗

arXiv2026

Micro-macro population dynamics models of benthic algae with long-memory decay and generic growth

Benthic algae as a primary producer in riverine ecosystems develop biofilms on the riverbed. Their population dynamics involve growth and decay processes, the former owing to the balance between biological proliferation and mortality, while the latter to mechanical abrasion because of the transport of sediment particles. Contrary to the assumptions of previous studies, the decay has experimentally been found to exhibit long-memory behavior, where the population decreases at an algebraic rate. However, the origin and mathematical theory of this phenomenon remain unresolved. The objective of this study is to introduce a novel mathematical model employing spin processes to describe microscopic biofilm dynamics. A spin process is a continuous-time jump process transitioning between states 0 and 1, and the continuum limit of these processes captures the long-memory decay and generates generic growth. The proposed framework leverages heterogeneous spin rates, achieved by appropriately superposing spin processes with distinct rates, to reproduce the long-memory decay. Computational simulations demonstrate the behavior of the model, particularly emphasizing rate-induced tipping phenomena. This mathematical model provides a computationally tractable interpretation of benthic algae dynamics and their long-term prediction, relevant to river-engineering applications.

math.PR↗

arXiv2026

Kolmogorov equations for evaluating the boundary hitting of degenerate diffusion with unsteady drift

Jacobi diffusion is a representative diffusion process whose solution is bounded in a domain under certain drift and diffusion coefficient conditions. However, the process without such conditions has not been thoroughly investigated. We explore a Jacobi diffusion whose drift coefficient is affected by another deterministic process, causing the process to hit the boundary of a domain in finite time. The Kolmogorov equation (a degenerate elliptic partial differential equation) for evaluating the boundary hitting of the proposed Jacobi diffusion is then presented and analyzed, with several conditional arguments, some of which are addressed computationally. We also investigate a related mean-field-type (McKean-Vlasov) self-consistent model arising in tourism management, where the drift depends on the index for sensor boundary hitting, thereby confining the process to a domain with higher probability. We propose a finite difference method for the linear and nonlinear Kolmogorov equations, which yields a unique numerical solution because of discrete ellipticity if the discount is positive. The accuracy of the finite difference method critically depends on the regularity of the boundary condition, and the use of high-order discretization is not always effective. Finally, we computationally investigate the mean field effect.

math.NA↗

arXiv2026

Multiple timescales in collective motion: daily and intraday upstream fish migration focusing on Feller condition

Fish migration is a collective phenomenon that has multiple timescales, ranging from daily to intraday (hourly or even finer). We propose a unified mathematical approach using diffusion bridges, nonlinear stochastic differential equations with pinned initial and terminal conditions, to model both daily and intraday fish migration phenomena. Drift and diffusion coefficients of these bridges are determined based on time-dependent parameterized average and variance curves fitted against fish count data, with which the unique existence of their solutions is rigorously guaranteed. We show that sample paths of the diffusion bridges have qualitatively distinctive properties depending on the Feller condition, namely, the ratio between the sizes of diffusion and drift. Our application study about the juvenile upstream migration of Plecoglossus altivelis altivelis (Ayu) in Japan clarifies similarities and differences between daily and intraday migration phenomena. Particularly, we discuss that the daily and intraday fish count data correspond to distinctive Feller indices, showing that the former is qualitatively less randomized and intermittent. The results obtained in this study suggest that the Feller condition potentially serves as an effective tool for evaluating fish migration phenomena of Ayu across different timescales.

q-bio.PE↗

arXiv2026

A Musielak-Orlicz approach for modeling uncertainties in long-memory processes

This paper proposes a novel mathematical framework for modeling uncertainties in supOU processes, a common model for long-memory phenomena. We address uncertainties as distortions in reversion and Levy measures, evaluating them simultaneously via state-dependent divergence functions on Musielak-Orlicz spaces. The core of our approach involves solving optimization problems to determine the upper- and lower-bounds of cumulants under a prescribed uncertainty set. Notably, we demonstrate that while classical measures like Kullback-Leibler divergence fail in this context, Musielak-Orlicz spaces effectively resolve these issues. Along with providing sufficient conditions for the well-posedness of these optimizations, we demonstrate the framework's practical utility through a water environmental application, modeling streamflow discharge. This work offers both a theoretical advancement and a robust tool for long-memory process analysis.

math.OC↗

arXiv2026

A rate-induced tipping in the Pearson diffusion

Rate-induced tipping is an instability that occurs in a system when its time-dependent rate parameter becomes larger than a threshold value. We investigate a Pearson diffusion process, a diffusion process having solutions staying in a bounded domain under certain conditions, whose noise-free limit experiences a rate-induced tipping such that solutions escape from the domain in a finite time. We show that the existence of noise leads to faster escapement from the domain.

math.PR↗

arXiv2026

Rate-induced tipping in a solvable model with the Allee effect

We present a novel exactly solvable ordinary differential equation model for rate-induced tipping: a dynamic phenomenon of dynamical systems where a time-dependent parameter triggers the transition of stability of a system. Our model contains an Allee effect that induces a saddle point and admits an explicit solution along with the extinction threshold of a time-dependent Allee parameter. More specifically, we derive an integral inequality that serves as a necessary condition for the occurrence of rate-induced tipping. A remarkable point in the proposed model is that it can handle population extinction such that the solution completely vanishes in a finite amount of time. An unconditionally stable cubature method suitable for our model is proposed, and its superiority over the classical forward Euler method is discussed. We also discuss a fisheries application where inland fisheries rose and fell from modern times to the present in Japan. The proposed model serves as a tractable mathematical tool for studying rate-induced tipping phenomena.

math.DS↗

arXiv2026

Non-negative diffusion bridge of the McKean-Vlasov type: analysis of singular diffusion and application to fish migration

The objective of this paper is to provide a new mathematical tool for fish migration that has not been studied well. McKean-Vlasov stochastic differential equations (MVSDEs) have broad potential applications in science and engineering, but remain insufficiently explored. We consider a non-negative McKean-Vlasov diffusion bridge, a diffusion process pinned at both initial and terminal times, motivated by diurnal fish migration phenomena. This type of MVSDEs has not been previously studied. Our particular focus is on a singular diffusion coefficient that blows up at the terminal time, which plays a role in applications of the proposed MVSDE to real fish migration data. We prove that the well-posedness of the MVSDE depends critically on the strength of the singularity in the diffusion coefficient. We present a sufficient condition under which the MVSDE admits a unique strong solution that is continuous and non-negative. We also apply the MVSDE to the latest fine fish count data with a 10-min time interval collected from 2023 to 2025 and computationally investigate these models. Thus, this study contributes to the formulation of a new non-negative diffusion bridge along with an application study.

math.PR↗

arXiv2026

Theoretical and computational investigations of superposed interacting affine and more complex processes

We theoretically and computationally investigate long-memory processes based on the Markovian lifts of affine jump-diffusion processes. A nominal superposition process consisting of an infinite number of interacting affine processes is considered, along with its finite-dimensional version and associated generalized Riccati equations. We propose a splitting scheme suited to the Markovian lifts where jump and diffusion parts are dealt with separately based on recently developed exact discretization methods. We examine the computational performance of the scheme through comparisons with the analytical results. We also numerically investigate a more complex model arising in the environmental sciences and some extended cases in which superposed processes belong to a class of nonlinear processes that generalize affine processes.

math.PR↗

arXiv2025

Two Issues in Modelling Fish Migration

Fish migration is a dynamic phenomenon observed in many surface water bodies on the earth, while its understanding is still insufficient. Particularly, the biological mechanism behind fish migration is not fully understood. Moreover, its observation is often conducted visually and hence manually, raising questions of accuracy and interpretation of the data sampled. We address the two issues, mechanism and observation, of fish migration based on a recently developed mathematical model. The results obtained in this short paper show that fish migration can be characterized through a minimization principle and evaluate the error of its manual observations. The minimization principle we hypothesize is an optimal control problem where the migrating fish population dynamically changes its size and fluctuation. We numerically investigate alternating and intensive observation schemes as case studies, demonstrating that in some realistic conditions the estimate of total fish count is not reliable. We believe that this paper contributes to a deeper understanding of fish migration.

q-bio.PE↗

arXiv2025

CIR bridge for modeling of fish migration on sub-hourly scale

Bridges, which are stochastic processes with pinned initial and terminal conditions, have recently been applied to various problems. We show that a bridge based on the Cox-Ingersoll-Ross process, called a CIR bridge in this paper, reasonably models the intraday number of migrating fish at an observation point in a river. The studied fish migrates between sunrise and sunset each day, which are considered the initial and terminal times, respectively. The CIR bridge is well-defined as a unique pathwise continuous solution to a stochastic differential equation with unbounded drift and diffusion coefficients and potentially represents the on-off intermittency of the fish count data. Our bridge is theoretically novel in that it admits closed-form time-dependent averages and variances, with which the model parameters can be identified efficiently, and is computable by a recently-developed one-step numerical method. The CIR bridge is applied to the sub-hourly migration data of the diadromous fish Plecoglossus altivelis altivelis in the Nagara River, Japan, from February to June.

math.PR↗