arXiv subjects

Chen Fei

Publications and source records attributed to Chen Fei.

9 recordsLinked to original sources

arXiv2025

A Task Equalization Allocation Algorithm Incorporating Blocking Estimation and Resource Similarity Analysis for Vehicle Control Real-Time Systems

In multi-core real-time vehicle control systems, synchronization blocking and resource contention pose critical challenges due to increasing task parallelism and shared resource access. These issues significantly degrade system schedulability and real-time performance, as traditional task allocation algorithms often overlook blocking impacts, leading to high scheduling failure rates under heavy loads. To address this, we propose the BR-WFD algorithm, which integrates blocking time estimation and resource similarity analysis. The algorithm minimizes global blocking overhead by prioritizing tasks with high synchronization sensitivity and aggregating shared-resource-accessing tasks onto the same core. Extensive simulations show that BR-WFD reduces required processor cores by 11\% to 28\% and maintains a 15\% to 20\% higher schedulable ratio compared to traditional methods under high-load and resource-competitive scenarios. This demonstrates its effectiveness in enhancing real-time performance and resource efficiency for multi-core task scheduling in intelligent driving systems.

cs.OS↗

arXiv2025

Research on Optimal Control Problem Based on Reinforcement Learning under Knightian Uncertainty

Considering that the decision-making environment faced by reinforcement learning (RL) agents is full of Knightian uncertainty, this paper describes the exploratory state dynamics equation in Knightian uncertainty to study the entropy-regularized relaxed stochastic control problem in a Knightian uncertainty environment. By employing stochastic analysis theory and the dynamic programming principle under nonlinear expectation, we derive the Hamilton-Jacobi-Bellman (HJB) equation and solve for the optimal policy that achieves a trade-off between exploration and exploitation. Subsequently, for the linear-quadratic (LQ) case, we examine the agent's optimal randomized feedback control under both state-dependent and state-independent reward scenarios, proving that the optimal randomized feedback control follows a Gaussian distribution in the LQ framework. Furthermore, we investigate how the degree of Knightian uncertainty affects the variance of the optimal feedback policy. Additionally, we establish the solvability equivalence between non-exploratory and exploratory LQ problems under Knightian uncertainty and analyze the associated exploration cost. Finally, we provide an LQ example and validate the theoretical findings through numerical simulations.

math.OC↗

arXiv2024

Positivity-preserving truncated Euler and Milstein methods for financial SDEs with super-linear coefficients

In this paper, we propose two variants of the positivity-preserving schemes, namely the truncated Euler-Maruyama (EM) method and the truncated Milstein scheme, applied to stochastic differential equations (SDEs) with positive solutions and super-linear coefficients. Under some regularity and integrability assumptions we derive the optimal strong convergence rates of the two schemes. Moreover, we demonstrate flexibility of our approaches by applying the truncated methods to approximate SDEs with super-linear coefficients (3/2 and Ai{\i}t-Sahalia models) directly and also with sub-linear coefficients (CIR model) indirectly. Numerical experiments are provided to verify the effectiveness of the theoretical results.

math.NA↗

arXiv2021

The truncated EM method for stochastic differential delay equations with variable delay

This paper mainly investigates the strong convergence and stability of the truncated Euler-Maruyama (EM) method for stochastic differential delay equations with variable delay whose coefficients can be growing super-linearly. By constructing appropriate truncated functions to control the super-linear growth of the original coefficients, we present a type of the truncated EM method for such SDDEs with variable delay, which is proposed to be approximated by the value taken at the nearest grid points on the left of the delayed argument. The strong convergence result (without order) of the method is established under the local Lipschitz plus generalized Khasminskii-type conditions and the optimal strong convergence order $1/2$ can be obtained if the global monotonicity with U function and polynomial growth conditions are added to the assumptions. Moreover, the partially truncated EM method is proved to preserve the mean-square and H_\infty stabilities of the true solutions. Compared with the known results on the truncated EM method for SDDEs, a better order of strong convergence is obtained under more relaxing conditions on the coefficients, and more refined technical estimates are developed so as to overcome the challenges arising due to variable delay. Lastly, some numerical examples are utilized to confirm the effectiveness of the theoretical results.

math.NA↗

arXiv2020

Delay-dependent Asymptotic Stability of Highly Nonlinear Stochastic Differential Delay Equations Driven by $G$-Brownian Motion

Based on the classical probability, the stability criteria for stochastic differential delay equations (SDDEs) where their coefficients are either linear or nonlinear but bounded by linear functions have been investigated intensively. Moreover, the dependent stability of the highly nonlinear hybrid stochastic differential equations is recently studied. In this paper, by using the nonlinear expectation theory, we explore the dependent stability of a class of highly nonlinear hybrid stochastic differential delay equations driven by $G$-Brownian motion ($G$-SDDEs). Firstly, we give preliminaries of sublinear expectation. Then, the delay-dependent criteria of the stability and boundedness of solutions to $G$-SDDEs is provided. Finally, an illustrative example is analyzed by the $φ$-max-mean algorithm.

math.OC↗

arXiv2019

Consistency of least squares estimation to the parameter for stochastic differential equations under distribution uncertainty

Under distribution uncertainty, on the basis of discrete data we investigate the consistency of the least squares estimator (LSE) of the parameter for the stochastic differential equation (SDE) where the noise are characterized by $G$-Brownian motion. In order to obtain our main result of consistency of parameter estimation, we provide some lemmas by the theory of stochastic calculus of sublinear expectation. The result shows that under some regularity conditions, the least squares estimator is strong consistent uniformly on the prior set. An illustrative example is discussed.

math.ST↗

arXiv2018

Generalized Ait-Sahalia-type interest rate model with Poisson jumps and convergence of the numerical approximation

In this paper, we consider the generalized Ait-Sahaliz interest rate model with Poisson jumps in finance. The analytical properties including the positivity, boundedness and pathwise asymptotic estimations of the solution to the model are investigated. Moreover, we prove that the Euler-Maruyama (EM) numerical solutions will converge to the true solution in probability. Finally, under assumption that the interest rate or the asset price is governed by this model, we apply the EM solutions to compute some financial quantities.

math.NA↗

arXiv2013

On exponential stability for stochastic differential equations disturbed by G-Brownian motion

We first introduce the calculus of Peng's G-Brownian motion on a sublinear expectation space $(Ω, {\cal H}, \hat{\mathbb{E}})$. Then we investigate the exponential stability of paths for a class of stochastic differential equations disturbed by a G-Brownian motion in the sense of quasi surely (q.s.). The analyses consist in G-Lyapunov function and some special inequalities. Various sufficient conditions are obtained to ensure the stability of strong solutions. In particular, by means of our results we generalize the one in the classical stochastic differential equations. Finally, an illustrative example is given.

math.PR↗

arXiv2013

Optimal stochastic control and optimal consumption and portfolio with G-Brownian motion

By the calculus of Peng's G-sublinear expectation and G-Brownian motion on a sublinear expectation space $(Ω, {\cal H}, \hat{\mathbb{E}})$, we first set up an optimality principle of stochastic control problem. Then we investigate an optimal consumption and portfolio decision with a volatility ambiguity by the derived verification theorem. Next the two-fund separation theorem is explicitly obtained. And an illustrative example is provided.

math.OC↗