相关论文: How to simulate L\'evy flights in a steep potentia…

By a coupling method, we prove that a family of stochastic partial differential equations (SPDEs) driven by highly degenerate pure jump L\'evy noises are exponential mixing. These pure jump L\'evy noises include $\alpha$-stable process with…

L\'evy stochastic processes, with noise distributed according to a L\'evy stable distribution, are ubiquitous in science. Focusing on the case of a particle trapped in an external harmonic potential, we address the problem of finding…

We propose a new higher-order time discretization scheme for the stochastic Navier--Stokes equations with additive noise, where its velocity and pressure approximates converge at strong rate $1.5$ in probability. The construction rests on…

We develop in this work a numerical method for stochastic differential equations (SDEs) with weak second order accuracy based on Gaussian mixture. Unlike the conventional higher order schemes for SDEs based on It\^o-Taylor expansion and…

We suggest a general framework for simulation of the triplet $(X_T,\bar X_ T,\tau_T)$ (L\'evy process, its extremum, and hitting time of the extremum), and, separately, $X_T,\bar X_ T$ and pairs $(X_T,\bar X_ T)$, $(\bar X_ T,\tau_T)$,…

The L\'evy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable…

This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…

This paper extends our recent results on multi-dimensional discrete-velocity models to the numerical level. By adopting an operator splitting scheme and introducing a suitable discrete Lyapunov function, we derive numerical control laws…

In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…

We introduce and compare computational techniques for sharp extreme event probability estimates in stochastic differential equations with small additive Gaussian noise. In particular, we focus on strategies that are scalable, i.e. their…

In this paper we propose a numerical scheme for the class of backward doubly stochastic (BDSDEs) with possible path-dependent terminal values. We prove that our scheme converge in the strong $L^2$-sense and derive its rate of convergence.…

In a high-frequency context, we investigate the efficient estimation of scaling and jump activity parameters for a stochastic differential equation driven by a L{\'e}vy process with both diffusion component and pure-jump component. We first…

We address numerical differentiation under coarse, non-uniform sampling and Gaussian noise. A maximum-likelihood estimator with $L_2$-norm constraint on a higher-order derivative is obtained, yielding spline-based solution. We introduce a…

Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…

In this paper we introduce a variable order time fractional differential equation driven by pure jump L\'evy noise, which models the motion of a particle exhibiting memory effect. We prove the well-posedness of this equation without…

In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…

This paper investigates the structure preservation and convergence analysis of a class of fully discrete finite difference schemes for the stochastic heat equation driven by L\'evy space-time white noise. The novelty lies in the…

We study a Monte Carlo algorithm for simulation of probability distributions based on stochastic step functions, and compare to the traditional Metropolis/Hastings method. Unlike the latter, the step function algorithm can produce an…

Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…

We analyze two-dimensional (2D) random systems driven by a symmetric L\'{e}vy stable noise which, under the sole influence of external (force) potentials $\Phi (x) $, asymptotically set down at Boltzmann-type thermal equilibria. Such…