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We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…

Optimization and Control · Mathematics 2025-05-27 Ashley Davey , Harry Zheng

The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation with globally Lipschitz continuous drift and diffusion coefficient. Recent results extend this convergence to coefficients which…

Numerical Analysis · Mathematics 2021-11-02 Martin Hutzenthaler , Arnulf Jentzen , Peter E. Kloeden

On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient. On the other…

Numerical Analysis · Mathematics 2012-09-13 Martin Hutzenthaler , Arnulf Jentzen , Peter E. Kloeden

This work focuses on the numerical approximations of neutral stochastic delay differential equations with their drift and diffusion coefficients growing super-linearly with respect to both delay variables and state variables. Under…

Numerical Analysis · Mathematics 2024-02-15 Jingjing Cai , Ziheng Chen , Yuanling Niu

We present an implicit Split-Step explicit Euler type Method (dubbed SSM) for the simulation of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts of superlinear growth in space, Lipschitz in measure and non-constant…

Numerical Analysis · Mathematics 2022-05-10 Xingyuan Chen , Goncalo dos Reis

In this paper we consider the numerical solutions for a class of jump diffusions with Markovian switching. After briefly reviewing necessary notions, a new jump-adapted efficient algorithm based on the Euler scheme is constructed for…

Numerical Analysis · Mathematics 2015-03-19 Jun Ye , Kai Li

We propose a new tamed Milstein-type scheme for stochastic differential equation with Markovian switching when drift coefficient is assumed to grow super-linearly. The strong rate of convergence is shown to be equal to $1.0$ under mild…

Probability · Mathematics 2019-09-18 Chaman Kumar , Tejinder Kumar

We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox-Ingersoll-Ross model, is multiplied by a (leverage) function of the spot price, its running maximum, and time.…

Computational Finance · Quantitative Finance 2018-10-09 Andrei Cozma , Christoph Reisinger

We consider in this work the convergence of a split-step Euler type scheme (SSM) for the numerical simulation of interacting particle Stochastic Differential Equation (SDE) systems and McKean-Vlasov Stochastic Differential Equations…

Probability · Mathematics 2023-03-28 Xingyuan Chen , Goncalo dos Reis

This paper studies the numerical approximation for McKean-Vlasov stochastic differential equations driven by L\'evy processes. We propose a tamed-adaptive Euler-Maruyama scheme and consider its strong convergence in both finite and infinite…

Probability · Mathematics 2024-01-09 Ngoc Khue Tran , Trung-Thuy Kieu , Duc-Trong Luong , Hoang-Long Ngo

This paper investigates the approximation of invariant measures for McKean-Vlasov stochastic differential equations (SDEs) using the Euler-Maruyama (EM) scheme under a monotonicity condition. Firstly, the convergence of the numerical…

Probability · Mathematics 2026-04-17 Zhen Wang , Mingyan Wu

We consider the use of adaptive timestepping to allow a strong explicit Euler-Maruyama discretisation to reproduce dynamical properties of a class of nonlinear stochastic differential equations with a unique equilibrium solution and…

Numerical Analysis · Mathematics 2017-06-13 Cónall Kelly , Alexandra Rodkina , Eeva Maria Rapoo

Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…

Probability · Mathematics 2012-05-24 Amarjit Budhiraja , Jiang Chen , Sylvain Rubenthaler

It is known in \cite{beccari} that the standard explicit Euler-type scheme (such as the exponential Euler and the linear-implicit Euler schemes) with a uniform timestep, though computationally efficient, may diverge for the stochastic…

Numerical Analysis · Mathematics 2023-11-14 Chuchu Chen , Tonghe Dang , Jialin Hong

This paper focuses on the strong convergence of the truncated $\theta$-Milstein method for a class of nonautonomous stochastic differential delay equations whose drift and diffusion coefficients can grow polynomially. The convergence rate,…

Numerical Analysis · Mathematics 2021-12-28 Shuaibin Gao , Junhao Hu , Jie He , Qian Guo

In this paper, we study functional type weak approximation of weak solutions of stochastic functional differential equations by means of the Euler--Maruyama scheme. Under mild assumptions on the coefficients, we provide a quantitative error…

Probability · Mathematics 2024-12-25 Yushi Hamaguchi , Dai Taguchi

The paper studies the rate of convergence of the weak Euler approximation for solutions to possibly completely degenerate SDEs driven by Levy processes, with Hoelder-continuous coefficients. It investigates the dependence of the rate on the…

Probability · Mathematics 2012-05-14 R. Mikulevicius

Stochastic differential equations (SDEs) on Riemannian manifolds have numerous applications in system identification and control. However, geometry-preserving numerical methods for simulating Riemannian SDEs remain relatively…

Numerical Analysis · Mathematics 2025-04-18 Xi Wang , Victor Solo

Extracting governing stochastic differential equation models from elusive data is crucial to understand and forecast dynamics for complex systems. We devise a method to extract the drift term and estimate the diffusion coefficient of a…

Numerical Analysis · Mathematics 2020-08-21 Jian Ren , Jinqiao Duan

We study the traditional backward Euler method for $m$-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H > 1/2$ whose drift coefficient satisfies the one-sided Lipschitz condition.…

Numerical Analysis · Mathematics 2022-05-30 Hao Zhou , Yaozhong Hu , Yanghui Liu