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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…
We propose and analyse a boundary-preserving numerical scheme for the weak approximation for some stochastic partial differential equations (SPDEs) with bounded state-space. We impose regularity assumptions on the drift and diffusion…
We present a novel solution method for It\^o stochastic differential equations (SDEs). We subdivide the time interval into sub-intervals, then we use the quadratic polynomials for the approximation between two successive intervals. The main…
We propose a modification of the standard linear implicit Euler integrator for the weak approximation of parabolic semilinear stochastic PDEs driven by additive space-time white noise. The new method can easily be combined with a finite…
We introduce a lattice random walk discretisation scheme for stochastic differential equations (SDEs) that samples binary or ternary increments at each step, suppressing complex drift and diffusion computations to simple 1 or 2 bit random…
This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…
We address the weak numerical solution of stochastic differential equations driven by independent Brownian motions (SDEs for short). This paper develops a new methodology to design adaptive strategies for determining automatically the…
Stochastic differential equations provide a rich class of flexible generative models, capable of describing a wide range of spatio-temporal processes. A host of recent work looks to learn data-representing SDEs, using neural networks and…
Construction of splitting-step methods and properties of related non-negativity and boundary preserving numerical algorithms for solving stochastic differential equations (SDEs) of Ito-type are discussed. We present convergence proofs for a…
Stochastic approximation (SA) and stochastic gradient descent (SGD) algorithms are work-horses for modern machine learning algorithms. Their constant stepsize variants are preferred in practice due to fast convergence behavior. However,…
This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractional diffusion operator to model the L\'{e}vy-type…
The paper deals with the numerical solution of the nonlinear Ito stochastic differential equations (SDEs) appearing in the unravelling of quantum master equations. We first develop an exponential scheme of weak order 1 for general globally…
In this paper, we study a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises. Our method consists in studying first the nonlocal SPDEs and showing then the convergence of the family of these…
We prove weak convergence of order one for a class of exponential based integrators for SDEs with non-globally Lipschtiz drift. Our analysis covers tamed versions of Geometric Brownian Motion (GBM) based methods as well as the standard…
In this paper we investigate quasi-stationary distributions {\mu}_N of stochastic approximation algorithms with constant step size which can be viewed as random perturbations of a time-continuous dynamical system. Inspired by ecological…
We investigate the stationary distribution of asymmetric and weakly asymmetric simple exclusion processes with open boundaries. We project the stationary distribution onto a subinterval, whose size is allowed to grow with the length of the…
We study an explicit exponential scheme for the time discretisation of stochastic Schr\"odinger equations driven by additive or multiplicative Ito noise. The numerical scheme is shown to converge with strong order $1$ if the noise is…
Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…
This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a self-similar fragmentation. Criteria for existence and…
In this paper, we address the question of the discretization of Stochastic Partial Differential Equations (SPDE's) for excitable media. Working with SPDE's driven by colored noise, we consider a numerical scheme based on finite differences…