Related papers: Stopped Brownian-increment tamed Euler method

This paper is devoted to order-one explicit approximations of random periodic solutions to multiplicative noise driven stochastic differential equations (SDEs) with non-globally Lipschitz coefficients. The existence of the random periodic…

In this paper we show that solutions of stochastic partial differential equations driven by Brownian motion can be approximated by stochastic partial differential equations forced by pure jump noise/random kicks. Applications to stochastic…

In this paper we consider multidimensional stochastic differential equations (SDEs) with discontinuous drift and possibly degenerate diffusion coefficient. We prove an existence and uniqueness result for this class of SDEs and we present a…

We consider the long-time behavior of an explicit tamed Euler scheme applied to a class of stochastic differential equations driven by additive noise, under a one-sided Lipschitz continuity condition. The setting encompasses drift…

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…

We consider the problem of numerically estimating expectations of solutions to stochastic differential equations driven by Brownian motions in the commonly occurring small noise regime. We consider (i) standard Monte Carlo methods combined…

Consider the following stochastic differential equation for $(X_t)_{t\ge 0}$ on $\mathbb R^d$ and its Euler-Maruyama (EM) approximation $(Y_{t_n})_{n\in \mathbb Z^+}$: \begin{align*} &d X_t=b( X_t) d t+\sigma(X_t) d B_t, \\ &…

The aim of this work is to provide the strong convergence results of numerical approximations of a general second order non-autonomous semilinear stochastic partial differential equation (SPDE) driven simultaneously by an additive…

In this paper, we consider numerical approximation to periodic measure of a time periodic stochastic differential equations (SDEs) under weakly dissipative condition. For this we first study the existence of the periodic measure $\rho_t$…

Inverse problems in scientific computing often require optimization over infinite-dimensional Hilbert spaces. A commonly used solver in such settings is stochastic gradient descent (SGD), where gradients are approximated using randomly…

We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We develop a comprehensive solution theory that…

In this paper, we study a class of super-linear stochastic differential delay equations with Poisson jumps (SDDEwPJs). The convergence and rate of the convergence of the truncated Euler-Maruyama numerical solutions to SDDEwPJs are…

In recent work of Hairer, Hutzenthaler and Jentzen, see [9], a stochastic differential equation (SDE) with infinitely often differentiable and bounded coefficients was constructed such that the Monte Carlo Euler method for approximation of…

This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean…

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…

We consider strong approximations of $1+1$-dimensional stochastic PDEs driven by additive space-time white noise. It has been long proposed (Davie-Gaines '01, Jentzen-Kloeden '08), as well as observed in simulations, that approximation…

Explicit discretizations of stochastic differential equations often encounter instability when the coefficients are not globally Lipschitz. The truncated schemes and tamed schemes have been proposed to handle this difficulty, but truncated…

This paper is concerned with the adaptive numerical treatment of stochastic partial differential equations. Our method of choice is Rothe's method. We use the implicit Euler scheme for the time discretization. Consequently, in each step, an…

We consider a mixed stochastic differential equation involving both standard Brownian motion and fractional Brownian motion with Hurst parameter $H>1/2$. The mean-square rate of convergence of Euler approximations of solution to this…

In this paper we study the existence and uniqueness of the strong solution of following d dimensional stochastic differential equation (SDE) driven by Brownian motion: dX(t)=b(t,X(t))dt+a(t,X(t))dB(t), X(0)= x, where B is a d-dimensional…