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

This paper focuses on explicit approximations for nonlinear stochastic delay differential equations (SDDEs). Under the weakly local Lipschitz and some suitable conditions, a generic truncated Euler-Maruyama (TEM) scheme for SDDEs is…

Coupling by reflection mixed with synchronous coupling is constructed for a class of stochastic differential equations (SDEs) driven by L\'{e}vy noises. As an application, we establish the exponential contractivity of the associated…

The rates of strong convergence for various approximation schemes are investigated for a class of stochastic differential equations (SDEs) which involve a random time change given by an inverse subordinator. SDEs to be considered are unique…

In this paper, by using Girsanov's transformation and the property of the corresponding reference stochastic differential equations, we investigate weak existence and uniqueness of solutions and weak convergence of Euler-Maruyama scheme to…

Let $(L_t)_{t \geq 0}$ be a $k$-dimensional L\'evy process and $\sigma: \mathbb{R}^d \to \mathbb{R}^{d \times k}$ a continuous function such that the L\'evy-driven stochastic differential equation (SDE) $$dX_t = \sigma(X_{t-}) \, dL_t,…

This work considers weak approximations of stochastic partial differential equations (SPDEs) driven by L\'evy noise. The SPDEs at hand are parabolic with additive noise processes. A weak-convergence rate for the corresponding Galerkin…

In this paper, we consider the averaging principle for a class of McKean-Vlasov stochastic differential equations with slow and fast time-scales. Under some proper assumptions on the coefficients, we first prove that the slow component…

The aim of the book is to present some recent results in the theory of stochastic It\^o equations with singular deterministic part (drift) and its applications to second-order elliptic and parabolic equations with singular first-order…

The strong convergence of Euler approximations of stochastic delay differential equations is proved under general conditions. The assumptions on drift and diffusion coefficients have been relaxed to include polynomial growth and only…

It is well known that both gradient descent and stochastic coordinate descent achieve a global convergence rate of $O(1/k)$ in the objective value, when applied to a scheme for minimizing a Lipschitz-continuously differentiable,…

In this paper, we deal with a class of reflected backward stochastic differential equations associated to the subdifferential operator of a lower semi-continuous convex function driven by Teugels martingales associated with L\'{e}vy…

Discrete approximations to the equation \begin{equation*} L_{cont}u = u^{(4)} + D(x) u^{(3)} + A(x) u^{(2)} + (A'(x)+H(x)) u^{(1)} + B(x) u = f, \; x\in[0,1] \end{equation*} are considered. This is an extension of the Sturm-Liouville case…

In this paper, we study the averaging principle for a class of stochastic differential equations driven by $\alpha$-stable processes with slow and fast time-scales, where $\alpha\in(1,2)$. We prove that the strong and weak convergence order…

We present a criterion for uniform in time convergence of the weak error of the Euler scheme for Stochastic Differential equations (SDEs). The criterion requires i) exponential decay in time of the space-derivatives of the semigroup…

In the present paper, we give some examples of stochastic differential equations which have delicateness in the Markov and strong Markov properties, the uniqueness locally in time and globally in time, and initial conditions. Moreover, we…

The paper estimates the rate of convergence of the weak Euler approximation for the solutions of SDEs with Hoelder continuous coefficients driven by point and martingale measures. The equation considered has a non-degenerate main part whose…

In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…

In this article, we investigate the convergence rate of the discrete-time Clark--Ocone formula provided by Akahori--Amaba--Okuma [1]. In that paper, they mainly focus on the $L_{2}$-convergence rate of the first-order error estimate related…

Constrained optimization problems where both the objective and constraints may be nonsmooth and nonconvex arise across many learning and data science settings. In this paper, we show for any Lipschitz, weakly convex objectives and…

We consider the 3D stochastic Navier-Stokes equation on the torus. Our main result concerns the temporal and spatio-temporal discretisation of a local strong pathwise solution. We prove optimal convergence rates in for the energy error with…