Related papers: Weak order in averaging principle for stochastic d…
The purpose of this paper is to establish asymptotic behaviors of time-inhomogeneous multi-scale stochastic differential equations (SDEs). To achieve them, we analyze the evolution system of measures for time-inhomogeneous Markov…
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 this paper we establish a comparison theorem for stochastic differential delay equations with jumps. An example is constructed to demonstrate that the comparison theorem need not hold whenever the diffusion term contains a delay function…
In this paper, we investigate the convergence rate of the averaging principle for stochastic differential equations (SDEs) with $\beta$-H\"older drift driven by $\alpha$-stable processes. More specifically, we first derive the Schauder…
We consider a class of stochastic processes with rough stochastic volatility, examples of which include the rough Bergomi and rough Stein-Stein model, that have gained considerable importance in quantitative finance. A basic question for…
We give sufficient Gordin-type criteria for the iterated (enhanced) weak invariance principle to hold for deterministic dynamical systems. Such an invariance principle is intrinsically related to the interpretation of stochastic integrals.…
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
In this paper, we consider a fundamental class of stochastic differential equations with time delays. Our aim is to investigate the weak convergence with respect to delay parameter of the solutions. Based on the techniques of Malliavin…
It is known from the monograph [1, Chapter 5] that the weak convergence analysis of numerical schemes for stochastic Maxwell equations is an unsolved problem. This paper aims to fill the gap by establishing the long-time weak convergence…
In this paper, we develop the averaging principle for a class of two-time-scale stochastic reaction-diffusion equations driven by Wiener processes and Poisson random measures. We assume that all coefficients of the equation have polynomial…
We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is…
We analyse the asymptotic properties of a continuous-time, two-timescale stochastic approximation algorithm designed for stochastic bilevel optimisation problems in continuous-time models. We obtain the weak convergence rate of this…
The averaging principle for slow-fast systems of various kind of stochastic (partial) differential equations has been extensively studied. An analogous result was shown for slow-fast systems of rough differential equations driven by random…
We study stochastic differential equations with jumps with no diffusion part. We provide some basic stochastic characterizations of solutions of the corresponding non-local partial differential equations and prove the Harnack inequality for…
We investigate the convergence of hitting times for jump-diffusion processes. Specifically, we study a sequence of stochastic differential equations with jumps. Under reasonable assumptions, we establish the convergence of solutions to the…
We consider a slow-fast stochastic process where the slow component is a jump process on a measurable index set whose transition rates depend on the position of the fast component. Between the jumps, the fast component evolves according to…
We are concerned about the averaging principle for the stochastic Burgers equation with slow-fast time scale. This slow-fast system is driven by L\'{e}vy processes. Under some appropriate conditions, we show that the slow component of this…
Given an It\=o semimartingale with a time-homogeneous jump part observed at high frequency, we prove weak convergence of a normalized truncated empirical distribution function of the L\'evy measure to a Gaussian process. In contrast to…
In this paper, we quantitative convergence in $W_2$ for a family of Langevin-like stochastic processes that includes stochastic gradient descent and related gradient-based algorithms. Under certain regularity assumptions, we show that the…
For a stochastic differential equation driven by a fractional Brownian motion with Hurst parameter $H> \frac12$ it is known that the classical Euler scheme has the rate of convergence $2H-1$. In this paper we introduce a new numerical…