Related papers: Infinite-dimensional stochastic differential equat…
We introduce a system of Brownian particles, each absorbed upon hitting an associated moving boundary. The boundaries are determined by the conditional probabilities of the particles being absorbed before some final time horizon, given the…
It is shown that in a large class of disordered systems with non-degenerate disorder, in presence of non-local interactions, the Integrated Density of States (IDS) is at least H\"older continuous in one dimension and universally infinitely…
We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. We focus on the case where the escape is degenerate in the sense that points from…
In this paper, we study a multidimensional backward stochastic differential equation (BSDE) with an additional rough drift (rough BSDE), and give the existence and uniqueness of the adapted solution, either when the terminal value and the…
We present a predictive local field theory for the nonequilibrium dynamics of interacting active Brownian particles with a spherical shape in two spatial dimensions. The theory is derived by a rigorous coarse-graining starting from the…
Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with widespread applications in several fields, e.g. in finance, in physics and biology. The definition of the process depends crucially on the…
This paper concerns with some of the results related to the singular solutions of certain types of non-linear integrable differential equations (NIDE) and behavior of the singularities of those equations. The approach heavily relies on the…
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…
This paper establishes results on the existence and uniqueness of solutions to McKean-Vlasov equations, also called mean-field stochastic differential equations, in an infinite-dimensional Hilbert space setting with irregular drift. Here,…
We investigate the dynamics of individual colloidal particles in a one-dimensional periodic potential using the intermediate scattering function (ISF) as a key observable. We elaborate a theoretical framework and derive formally exact…
We consider a discrete particle system of two species coupled through nonlocal interactions driven by the one-dimensional Newtonian potential, with repulsive self-interaction and attractive cross-interaction. After providing a suitable…
We investigate a system of Brownian particles weakly bound by attractive parity-symmetric potentials that grow at large distances as $V(x) \sim |x|^\alpha$, with $0 < \alpha < 1$. The probability density function $P(x,t)$ at long times…
We consider infinite-dimensional random diffusion dynamics for the Asakura--Oosawa model of interacting hard spheres of two different sizes. We construct a solution to the corresponding SDE with collision local times, analyse its reversible…
Although statistical inference in stochastic differential equations (SDEs) driven by Wiener process has received significant attention in the literature, inference in those driven by fractional Brownian motion seem to have seen much less…
We review recent progress in the study of infinite-dimensional stochastic differential equations with symmetry. This paper contains examples arising from random matrix theory.
We consider the one-dimensional squared Bessel process given by the stochastic differential equation (SDE) \begin{align*} dX_t = 1\,dt + 2\sqrt{X_t}\,dW_t, \quad X_0=x_0, \quad t\in[0,1], \end{align*} and study strong (pathwise)…
The purpose of this paper is to analyze solutions of a non-local nonlinear partial integro-differential equation (PIDE) in multidimensional spaces. Such class of PIDE often arises in financial modeling. We employ the theory of abstract…
We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…
Given a stochastic differential equation (SDE) in $\mathbb{R}^n$ whose solution is constrained to lie in some manifold $M \subset \mathbb{R}^n$, we propose a class of numerical schemes for the SDE whose iterates remain close to $M$ to high…
In this paper, we study the existence of random periodic solutions for semilinear stochastic differential equations. We identify them as solutions of coupled forward-backward infinite horizon stochastic integral equations (IHSIEs), using…