Related papers: Convergence in Density of Splitting AVF Scheme for…
This paper is concerned with the numerical analysis of the explicit upwind finite volume scheme for numerically solving continuity equations. We are interested in the case where the advecting velocity field has spatial Sobolev regularity…
This work is devoted to convergence analysis of an exponential integrator scheme for semi-discretization in time of nonlinear stochastic wave equation. A unified framework is first set forth, which covers important cases of additive and…
In this paper we study the randomized non-autonomous complete linear differential equation. The diffusion coefficient and the source term in the differential equation are assumed to be stochastic processes and the initial condition is…
We develop a novel class of MCMC algorithms based on a stochastized Nesterov scheme. With an appropriate addition of noise, the result is a time-inhomogeneous underdamped Langevin equation, which we prove emits a specified target…
Colloidal particles that experience perfectly elastic collisions can be modelled using Langevin processes with specular reflection conditions. The article presents a discretisation scheme and offers a conjecture for the rate of convergence…
We consider stochastic differential equations of the form $dY_t=V(Y_t)\,dX_t+V_0(Y_t)\,dt$ driven by a multi-dimensional Gaussian process. Under the assumption that the vector fields $V_0$ and $V=(V_1,\ldots,V_d)$ satisfy H\"{o}rmander's…
In this paper, we present a generic methodology for the efficient numerical approximation of the density function of the McKean-Vlasov SDEs. The weak error analysis for the projected process motivates us to combine the iterative Multilevel…
We establish an optimal strong convergence rate of a fully discrete numerical scheme for second order parabolic stochastic partial differential equations with monotone drifts, including the stochastic Allen-Cahn equation, driven by an…
Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework for assessing the quality of such a sampling scheme corresponds to smooth and strongly log-concave…
Consider stochastic functional differential equations, whose coefficients depend on past histories. The solution determines a non-Markov process. In the present paper, we shall obtain the existence of smooth densities for joint…
We consider the one-dimensional outer stochastic Stefan problem with reflection. The problem admits maximal solutions as long as the velocity of the moving boundary remains bounded, [3,9,10]. We apply Malliavin calculus to the transformed…
The Average Vector Field (AVF) method is a B-series scheme of the second order. As a discrete gradient method it preserves exactly the energy integral for any canonical Hamiltonian system. We present and discuss two locally exact and…
We study smoothness of densities for the solutions of SDEs whose coefficients are smooth and nondegenerate only on an open domain $D$. We prove that a smooth density exists on $D$ and give upper bounds for this density. Under some…
Adaptive Multilevel Splitting (AMS for short) is a generic Monte Carlo method for Markov processes that simulates rare events and estimates associated probabilities. Despite its practical efficiency, there are almost no theoretical results…
We investigate the estimates of the density for the traditional Euler-Maruyama discretization of stochastic differential equations (SDEs) with multiplicative noise. Our estimates focus on two key aspects: (1) the $L^p$-upper bounds for…
The study of accurate methods to estimate the distribution of stellar rotational velocities is important for understanding many aspects of stellar evolution. From such observations we obtain the projected rotational speed v sin(i) in order…
We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability measures which includes an interaction term. Our main insight…
This paper discusses the spectral collocation method for numerically solving nonlocal problems: one dimensional space fractional advection-diffusion equation; and two dimensional linear/nonlinear space fractional advection-diffusion…
In this paper, we propose and analyze an adaptive time-stepping fully discrete scheme which possesses the optimal strong convergence order for the stochastic nonlinear Schr\"odinger equation with multiplicative noise. Based on the splitting…
We show regularity properties of local densities of solutions of stochastic differential equations (SDEs) with the Fourier analytic approach. With this simple method, statements that were previously derived with approaches using Malliavin…