相关论文: First order convergence of weak Wong--Zakai approx…

We study stochastic differential equations (SDEs) with multiplicative Stratonovich-type noise of the form $ dX_t = b(X_t) dt + \sigma(X_t)\circ d W_t, X_0=x_0\in\mathbb{R}^d, t\geq0,$ with a possibly singular drift $b\in…

In this paper, we study the diffusion approximation for slow-fast stochastic differential equations with state-dependent switching, where the slow component $X^{\varepsilon}$ is the solution of a stochastic differential equation with…

In this paper, a combination of Galerkin's method and Dafermos' transformation is first used to prove the existence and uniqueness of solutions for a class of stochastic nonlocal PDEs with long time memory driven by additive noise. Next,…

This paper investigates the convergence of Wong--Zakai approximations to regime-switching stochastic differential equations, generated by a collection of finite-variation approximations to Brownian motion. We extend the results of Nguyen…

We investigate the stochastic modified equation which plays an important role in the stochastic backward error analysis for explaining the mathematical mechanism of a numerical method. The contribution of this paper is threefold. First, we…

We present a method for approximating solutions of Stochastic Differential Equations (SDEs) with arbitrary rates. This approximation is derived for bounded and measurable test functions. Specifically, we demonstrate that, leveraging the…

This paper develops an $\alpha$-parametrized framework for analyzing the strong convergence of the stochastic theta (ST) method for stochastic differential equations driven by time-changed L\'evy noise (TCSDEwLNs) with time-space-dependent…

A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations by general one step methods is proved, which is an extension of a theorem due to Milstein. As an application, uniform second…

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…

The convergence of the first order Euler scheme and an approximative variant thereof, along with convergence rates, are established for rough differential equations driven by c\`adl\`ag paths satisfying a suitable criterion, namely the…

For equations $ x'(t) = -x(t) + \zeta f(x(t-h)), x \in \R, f'(0)= -1, \zeta > 0,$ with $C^3$-nonlinearity $f$ which has negative Schwarzian derivative and satisfies $xf(x) < 0$ for $x\not=0$, we prove convergence of all solutions to zero…

It is known that the transition probabilities of a solution to a classical It\^o stochastic differential equation (SDE) satisfy in the weak sense the associated Kolmogorov equation. The Kolmogorov equation is a partial differential equation…

The aim of this paper is to obtain convergence in mean in the uniform topology of piecewise linear approximations of Stochastic Differential Equations (SDEs) with $C^1$ drift and $C^2$ diffusion coefficients with uniformly bounded…

In this paper, we obtained the strong convergence of Wong-Zakai approximations of reflected SDEs in a general multidimensional domain giving an affirmative answer to the question posed in [ES].

We study the convergence of higher order schemes for the Cauchy problem associated to the KdV equation. More precisely, we design a Galerkin type implicit scheme which has higher order accuracy in space and first order accuracy in time. The…

In this article we study a class of stochastic functional differential equations driven by L\'{e}vy processes (in particular, $\alpha$-stable processes), and obtain the existence and uniqueness of Markov solutions in small time intervals.…

Let $d \ge 2$. In this paper, we study weak solutions for the following type of stochastic differential equation \[ dX_{t}=dS_{t}+b(s+t, X_{t})dt, \quad X_{0}=x, \] where $(s,x)\in \mathbb{R}_+ \times \mathbb{R}^{d}$ is the initial starting…

We establish a unconditional and optimal strong convergence rate of Wong--Zakai type approximations in Banach space norm for a parabolic stochastic partial differential equation with monotone drift, including the stochastic Allen--Cahn…

We present a numerical method for the approximation of solutions for the class of stochastic differential equations driven by Brownian motions which induce stochastic variation in fixed directions. This class of equations arises naturally…

In this paper we study weak solutions for the following type of stochastic differential equation \[ dX_{t}=dW_{t}+b(t, X_{t})dt, \quad t\ge s, \quad X_{s}=x, \] where $b: [0,\infty) \times \mathbb{R}^{d} \to \mathbb{R}^{d}$ is a measurable…