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

The nonlinear gyrokinetic equations describe plasma turbulence in laboratory and astrophysical plasmas. To solve these equations, massively parallel codes have been developed and run on present-day supercomputers. This paper describes…

We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise, where Langevin representation is absent. In view of the L\'{e}vy noise sensitivity to environmental inhomogeneities, the pertinent random…

This paper develops a novel weak multilevel Monte-Carlo (MLMC) approximation scheme for L\'evy-driven Stochastic Differential Equations (SDEs). The scheme is based on the state space discretization (via a continuous-time Markov chain…

Complex dynamical systems which are governed by anomalous diffusion often can be described by Langevin equations driven by L\'evy stable noise. In this article we generalize nonlinear stochastic differential equations driven by Gaussian…

We propose numerical schemes for the approximate solution of problems defined on the edges of a one-dimensional graph. In particular, we consider linear transport and a drift-diffusion equations, and discretize them by extending Finite…

This article describes methods for the deterministic simulation of the collisional Boltzmann equation. It presumes that the transport and collision parts of the equation are to be simulated separately in the time domain. Time stepping…

We develop a scale-invariant truncated L\'evy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits L\'evy stability for the probability density, and hence shows scaling…

Pure-jump L\'evy processes are popular classes of stochastic processes which have found many applications in finance, statistics or machine learning. In this paper, we propose a novel family of self-decomposable L\'evy processes where one…

This paper studies the numerical approximation for McKean-Vlasov stochastic differential equations driven by L\'evy processes. We propose a tamed-adaptive Euler-Maruyama scheme and consider its strong convergence in both finite and infinite…

We study parameter estimation for univariate stochastic differential equations with locally Lipschitz drift and H\"older continuous multiplicative diffusion, a class commonly arising in several applications. Existing inference methods…

General stochastic equations with jumps are studied. We provide criteria for the uniqueness and existence of strong solutions under non-Lipschitz conditions of Yamada-Watanabe type. The results are applied to stochastic equations driven by…

This paper studies a class of optimal multiple stopping problems driven by L\'evy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real…

The kinetic Langevin dynamics finds diverse applications in various disciplines such as molecular dynamics and Hamiltonian Monte Carlo sampling. In this paper, a novel splitting scalar auxiliary variable (SSAV) scheme is proposed for the…

We consider the long-time behavior of an explicit tamed Euler scheme applied to a class of stochastic differential equations driven by additive noise, under a one-sided Lipschitz continuity condition. The setting encompasses drift…

We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…

New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic differential…

This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These…

This article analyzes an explicit temporal splitting numerical scheme for the stochastic Allen-Cahn equation driven by additive noise, in a bounded spatial domain with smooth boundary in dimension $d\le 3$. The splitting strategy is…

Sticky diffusion models a Markovian particle experiencing reflection and temporary adhesion phenomena at the boundary. Numerous numerical schemes exist for approximating stopped or reflected stochastic differential equations (SDEs), but…

We present a method for constructing numerical schemes with up to 3rd strong convergence order for solution of a class of stochastic differential equations, including equations of the Langevin type. The construction proceeds in two stages.…