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In this paper, we introduce adaptive Euler-Maruyama schemes for McKean-Vlasov stochastic differential equations (SDEs) assuming only a standard monotonicity condition on the drift and diffusion coefficients but no global Lipschitz…

Numerical Analysis · Mathematics 2021-11-02 Christoph Reisinger , Wolfgang Stockinger

In this paper, we investigate the problem of strong approximation of the solutions of stochastic differential equations (SDEs) when the drift coefficient is given in integral form. We investigate its upper error bounds, in terms of the…

Numerical Analysis · Mathematics 2025-11-20 Paweł Przybyłowicz , Michał Sobieraj

An implicit Euler--Maruyama method with non-uniform step-size applied to a class of stochastic partial differential equations is studied. A spectral method is used for the spatial discretization and the truncation of the Wiener process. A…

Numerical Analysis · Mathematics 2018-04-11 Yoshihito Kazashi

Consider the following stochastic differential equation driven by multiplicative noise on $\mathbb{R}^d$ with a superlinearly growing drift coefficient, \begin{align*} \mathrm{d} X_t = b (X_t) \, \mathrm{d} t + \sigma (X_t) \, \mathrm{d}…

Probability · Mathematics 2025-05-07 Xiang Li , Yingjun Mo , Haoran Yang

We study the strong convergence order of the Euler-Maruyama scheme for scalar stochastic differential equations with additive noise and irregular drift. We provide a general framework for the error analysis by reducing it to a weighted…

Probability · Mathematics 2020-11-03 Andreas Neuenkirch , Michaela Szölgyenyi

We propose an {\em implementable} numerical scheme for the discretization of linear-quadratic optimal control problems involving SDEs in higher dimensions with {\em control constraint}. For time discretization, we employ the implicit Euler…

Analysis of PDEs · Mathematics 2024-12-12 Abhishek Chaudhary

In this paper, we establish the weak convergence rate of density-dependent stochastic differential equations with bounded drift driven by $\alpha$-stable processes with $\alpha\in(1,2)$. The well-posedness of these equations has been…

Probability · Mathematics 2024-06-03 Ke Song , Zimo Hao

The Ensemble Kalman methodology in an inverse problems setting can be viewed as an iterative scheme, which is a weakly tamed discretization scheme for a certain stochastic differential equation (SDE). Assuming a suitable approximation…

Probability · Mathematics 2018-06-19 Dirk Blömker , Claudia Schillings , Philipp Wacker

A new class of explicit Euler schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that these…

Probability · Mathematics 2016-09-05 Sotirios Sabanis

We study the weak convergence of a generic tamed Euler-Maruyama scheme for kinetic stochastic differential equations (SDEs) with integrable drifts. We show that the marginal density of the considered scheme converges at rate 1/2 to the…

Probability · Mathematics 2026-03-25 Zimo Hao , Khoa Lê , Chengcheng Ling

Electron collisions, described by stochastic differential equations (SDEs), were simulated using a second-order weak convergence algorithm. Using stochastic analysis, we constructed an SDE for energetic electrons in Lorentz plasma to…

Plasma Physics · Physics 2018-11-15 Wentao Wu , Jian Liu , Hong Qin

We propose an algorithm for approximating the solution of a strongly oscillating SDE, that is, a system in which some ergodic state variables evolve quickly with respect to the other variables. The algorithm profits from homogenization…

Probability · Mathematics 2015-03-19 Camilo Andrés García Trillos

In this paper, we study the Euler--Maruyama scheme for a particle method to approximate the McKean--Vlasov dynamics of calibrated local-stochastic volatility (LSV) models. Given the open question of well-posedness of the original problem,…

Computational Finance · Quantitative Finance 2023-09-04 Christoph Reisinger , Maria Olympia Tsianni

The truncated Euler-Maruyama (EM) method is proposed to approximate a class of non-autonomous stochastic differential equations (SDEs) with the H\"older continuity in the temporal variable and the super-linear growth in the state variable.…

Numerical Analysis · Mathematics 2019-07-19 Wei Liu , Xuerong Mao , Jingwen Tang , Yue Wu

In this paper, we consider the weak convergence of the Euler-Maruyama approximation for one dimensional stochastic differential equations involving the local times of the unknown process. We use a transformation in order to remove the local…

Numerical Analysis · Mathematics 2017-01-18 Mohsine Benabdallah , Kamal Hiderah

We describe an Euler scheme to approximate solutions of L\'evy driven Stochastic Differential Equations (SDE) where the grid points are random and given by the arrival times of a Poisson process. This result extends a previous work of the…

Probability · Mathematics 2013-09-10 Albert Ferreiro-Castilla , Andreas E Kyprianou , Robert Scheichl

We consider a class of general SDEs with a jump integral term driven by a time-inhomogeneous Poisson random measure. We propose a two-parameters Euler-type scheme for this SDE class and prove an optimal rate for the strong convergence with…

Probability · Mathematics 2025-08-07 Mireille Bossy , Paul Maurer

This paper focuses on the numerical scheme for multiple-delay stochastic differential equations with partially H\"older continuous drifts and locally H\"older continuous diffusion coefficients. To handle with the superlinear terms in…

Numerical Analysis · Mathematics 2024-03-19 Zhuoqi Liu , Zhaohang Wang , Siying Sun , Shuaibin Gao

This article introduces and analyzes a new explicit, easily implementable, and full discrete accelerated exponential Euler-type approximation scheme for additive space-time white noise driven stochastic partial differential equations…

Probability · Mathematics 2020-06-04 Martin Hutzenthaler , Arnulf Jentzen , Diyora Salimova

Consider the following stochastic differential equation (SDE) $$dX_t = b(t,X_{t-}) \, dt+ dL_t, \quad X_0 = x,$$ driven by a $d$-dimensional L\'evy process $(L_t)_{t \geq 0}$. We establish conditions on the L\'evy process and the drift…

Probability · Mathematics 2020-05-01 Franziska Kühn , René L. Schilling