相关论文: Computation of the invariant measure for a L\'{e}v…

SDE driven by an $\alpha $-stable process, $\alpha \in \lbrack 1,2),$ with Lipshitz continuous coefficient and $\beta $-H\"older drift is considered. The existence and uniqueness of a strong solution is proved when $\beta >1-\alpha /2$ by…

We construct a nonstandard finite difference numerical scheme to approximate stochastic differential equations (SDEs) using the idea of weighed step introduced by R.E. Mickens. We prove the strong convergence of our scheme under locally…

The understanding of adaptive algorithms for SDEs is an open area where many issues related to both convergence and stability (long time behaviour) of algorithms are unresolved. This paper considers a very simple adaptive algorithm, based…

We study the strong approximation of the solutions to singular stochastic kinetic equations (also referred to as second-order SDEs) driven by $\alpha$-stable processes, using an Euler-type scheme inspired by [11]. For these equations, the…

This paper explores the rates of convergence of solutions for multivariate stochastic differential equations (SDEs) driven by L\'evy processes within the small-time stable domain of attraction (DoA). Explicit bounds are derived for the…

This paper is concerned with strong convergence of the truncated Euler-Maruyama scheme for neutral stochastic differential delay equations driven by Brownian motion and pure jumps respectively. Under local Lipschitz condition, convergence…

We study the temporal-spatial regularity properties of tamed Euler approximations for L\'evy-driven SDEs with superlinearly growing drift and diffusion coefficients. We first introduce a novel tamed Euler-type scheme and establish its…

In this paper we deal with pointwise approximation of solutions of stochastic differential equations (SDEs) driven by infinite dimensional Wiener process with additional jumps generated by Poisson random measure. The further investigations…

For the stochastic differential equation (SDE) which has piecewise continuous arguments (PCAs), is driven by multiplicative noises and its drift coefficients are dissipative, we show that the solution at integer time is a Markov chain and…

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…

In this paper, we are concerned with a modified Euler scheme for the SDE under consideration, where the drift is of super-linear growth and dissipative merely outside a closed ball. By adopting the synchronous coupling, along with the…

We study the $L^1$-approximation of the log-Heston SDE at the terminal time point by arbitrary methods that use an equidistant discretization of the driving Brownian motion. We show that such methods can achieve at most order $ \min \{ \nu,…

We consider a general class of high order weak approximation schemes for stochastic differential equations driven by L\'evy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the…

In this paper, we investigate the optimal strong convergence rate of numerical approximations for the Cox--Ingersoll--Ross model driven by fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. To deal with the difficulties caused…

This article investigates the weak approximation towards the invariant measure of semi-linear stochastic differential equations (SDEs) under non-globally Lipschitz coefficients. For this purpose, we propose a linear-theta-projected Euler…

In this article, we consider the so-called modified Euler scheme for stochastic differential equations (SDEs) driven by fractional Brownian motions (fBm) with Hurst parameter $\frac13<H<\frac12$. This is a first-order time-discrete…

In the recent article [Hairer, M., Hutzenthaler, M., Jentzen, A., Loss of regularity for Kolmogorov equations, Ann. Probab. 43 (2015), no. 2, 468--527] it has been shown that there exist stochastic differential equations (SDEs) with…

We study the $L^1$-approximation of the log-Heston SDE at equidistant time points by Euler-type methods. We establish the convergence order $ 1/2-\epsilon$ for $\epsilon >0$ arbitrarily small, if the Feller index $\nu$ of the underlying CIR…

We present a new algorithms to discretize a decoupled forward backward stochastic differential equations driven by pure jump L\'evy process (FBSDEL in short). The method is built in two steps. Firstly, we approximate the FBSDEL by a forward…

We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the discontinuity of the drift coefficient we construct an…