Related papers: Infinite-dimensional stochastic differential equat…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
We study the equilibrium statistical mechanics of classical two-dimensional Coulomb systems living on a pseudosphere (an infinite surface of constant negative curvature). The Coulomb potential created by one point charge exists and goes to…
The classical models for irreversible diffusion-influenced reactions can be derived by introducing absorbing boundary conditions to over-damped continuous Brownian motion (BM) theory. As there is a clear corresponding stochastic process,…
We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…
We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called stochastic modified…
This paper focuses on the numerical scheme for delay-type stochastic McKean-Vlasov equations (DSMVEs) driven by fractional Brownian motion with Hurst parameter $H\in (0,1/2)\cup (1/2,1)$. The existence and uniqueness of the solutions to…
We consider suitable weak solutions of 2-dimensional Euler equations on bounded domains, and show that the class of completely random measures is infinitesimally invariant for the dynamics. Space regularity of samples of these random fields…
This paper is concerned with the long time behavior of Langevin dynamics of {\em Coulomb gases} in $\mathbf{R}^d$ with $d\geq 2$, that is a second order system of Brownian particles driven by an external force and a pairwise repulsive…
We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial…
We introduce a new method, which we call stochastic fusion, which takes an exclusion process and constructs an interacting particle systems in which more than one particle may occupy a lattice site. The construction only requires the…
Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…
Recently, it has been shown in [Jentzen, A., M\"uller-Gronbach, T., and Yaroslavtseva, L., Commun. Math. Sci., 14, 2016] that there exists a system of autonomous stochastic differential equations (SDE) on the time interval $[0,T]$ with…
We present a fluctuating boundary integral method (FBIM) for overdamped Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid particles of complex shape immersed in a Stokes fluid. We develop a novel approach for…
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surrogate models of the fine scale dynamics. We approximate the…
In this article, we study a weighted particle representation for a class of stochastic partial differential equations with Dirichlet boundary conditions. The locations and weights of the particles satisfy an infinite system of stochastic…
The quantum phase transition of the one-dimensional long-range transverse-field Ising model is explored by combining the quantum Monte Carlo method and stochastic parameter optimization, specifically achieved by tuning correlation ratios so…
We present a numerical method for the approximation of solutions for the class of stochastic differential equations driven by Brownian motions which induce stochastic variation in fixed directions. This class of equations arises naturally…
Lately, many phenomena in both applied and abstract mathematics and related disciplines have been expressed in terms of high order and fractional PDEs. Recently, Allouba introduced the Brownian-time Brownian sheet (BTBS) and connected it to…
Einstein-Smoluchowski diffusion, damped harmonic oscillations, and spatial decoherence are special cases of an elegant class of Markovian quantum Brownian motion models that is invariant under linear symplectic transformations. Here we…
The quantum jump approach, where pairs of state vectors follow Stochastic Schroedinger Equation (SSE) in order to treat the exact quantum dynamics of two interacting systems, is first described. In this work the non-uniqueness of such…