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In this work, we propose a new stochastic domain decomposition method for solving steady-state partial differential equations (PDEs) with random inputs. Based on the efficiency of the Variable-separation (VS) method in simulating stochastic…

Numerical Analysis · Mathematics 2025-02-06 Liang Chen , Yaru Chen , Qiuqi Li , Zhiwen Zhang

We investigate the conditional McKean-Vlasov stochastic differential equations with jumps and Markovian regime-switching. We establish the strong wellposedness using L2-Wasser-stein distance on the Wasserstein space. Also, we establish the…

Probability · Mathematics 2023-04-18 Jinghai Shao , Taoran Tian , Shen Wang

Stochastic differential equations (SDEs) are one of the most important representations of dynamical systems. They are notable for the ability to include a deterministic component of the system and a stochastic one to represent random…

Machine Learning · Computer Science 2021-05-19 Noura Dridi , Lucas Drumetz , Ronan Fablet

This paper is dedicated to investigating the adaptive Euler-Maruyama (EM) schemes for the approximation of McKean-Vlasov stochastic differential equations (SDEs) with common noise. When the drift and diffusion coefficients both satisfy the…

Numerical Analysis · Mathematics 2025-09-03 Hu Liu , Shuaibin Gao , Junhao Hu

Pathwise uniqueness for multi-dimensional stochastic McKean--Vlasov equation is established under moderate regularity conditions on the drift and diffusion coefficients. Both drift and diffusion depend on the marginal measure of the…

Probability · Mathematics 2023-01-02 Alexander Veretennikov

We study the long time behavior of the solution to some McKean-Vlasov stochastic differential equation (SDE) driven by a Poisson process. In neuroscience, this SDE models the asymptotic dynamic of the membrane potential of a spiking neuron…

Probability · Mathematics 2020-08-17 Quentin Cormier , Etienne Tanré , Romain Veltz

In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…

Probability · Mathematics 2024-03-27 Kai Du , Yunzhang Li , Yuyang Ye

Via constructing an asymptotic coupling by reflection, in this paper we establish uniform-in-time estimates on probability distances for mean-field type SDEs, where the drift terms under consideration are dissipative merely in the long…

Probability · Mathematics 2024-09-26 Jianhai Bao , Jiaqing Hao

We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…

Machine Learning · Statistics 2020-06-29 Martin Jørgensen , Marc Peter Deisenroth , Hugh Salimbeni

We present an explicit method for simulating stochastic differential equations (SDEs) that have variable diffusion coefficients and satisfy the detailed balance condition with respect to a known equilibrium density. In Tupper and Yang…

Numerical Analysis · Mathematics 2014-06-27 Paul Tupper , Xin Yang

In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…

Methodology · Statistics 2025-07-01 Ziyuan Chen , Shunxing Yan , Fang Yao

A challenge in multivariate problems with discrete structures is the inclusion of prior information that may differ in each separate structure. A particular example of this is seismic amplitude versus angle (AVA) inversion to elastic…

Methodology · Statistics 2012-08-09 Erlend Aune , Daniel Simpson

We propose a novel projection-based particle method for solving the McKean-Vlasov stochastic differential equations. Our approach is based on a projection-type estimation of the marginal density of the solution in each time step. The…

Numerical Analysis · Mathematics 2018-08-07 Denis Belomestny , John Schoenmakers

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

Computer Vision and Pattern Recognition · Computer Science 2024-08-26 Defang Chen , Zhenyu Zhou , Jian-Ping Mei , Chunhua Shen , Chun Chen , Can Wang

We consider controlled stochastic differential equations (SDEs) with measurable coefficients, a uniformly elliptic diffusion coefficient and an $L_d$-drift. No space-regularity will be assumed for the coefficients. In this framework we…

Analysis of PDEs · Mathematics 2025-09-19 David Criens

For a class of McKean-Vlasov stochastic differential equations with singular interactions, which include the Coulomb/Riesz/Biot-Savart kernels as typical examples (Examples 2.1 and 2.2), we derive the well-posedness and regularity estimates…

Probability · Mathematics 2026-04-20 Xing Huang , Panpan Ren , Feng-Yu Wang

In this paper, existence and uniqueness are proved for path-dependent McKean-Vlasov type SDEs with integrability conditions. Gradient estimates and Harnack type inequalities are derived in the case that the coefficients are Dini continuous…

Probability · Mathematics 2019-02-26 Xing Huang

We present a comprehensive discretization scheme for linear and nonlinear stochastic differential equations (SDEs) driven by either Brownian motions or $\alpha$-stable processes. Our approach utilizes compound Poisson particle…

Probability · Mathematics 2023-07-14 Xicheng Zhang

We analyse a Monte Carlo particle method for the simulation of the calibrated Heston-type local stochastic volatility (H-LSV) model. The common application of a kernel estimator for a conditional expectation in the calibration condition…

Computational Finance · Quantitative Finance 2025-04-22 Christoph Reisinger , Maria Olympia Tsianni

This paper investigates first the existence and uniqueness of solutions for McKean-Vlasov forward-backward doubly stochastic differential equations (MV-FBDSDEs) in infinite-dimensional real separable Hilbert spaces. These equations combine…

Probability · Mathematics 2024-07-15 AbdulRahman Al-Hussein , Abdelhakim Ninouh , Boulakhras Gherbal