Related papers: Forward and Backward Stochastic Differential Equat…
In this paper, we study the backward stochastic differential equations driven by G-Brownian motion with double mean reflections, which means that the constraints are made on the law of the solution. Making full use of the backward Skorokhod…
This paper is intended to give a representation for stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use its connection with reflected generalized…
In this paper, a solution is given to reflected backward doubly stochastic differential equations when the barrier is not necessarily right-continuous, and the noise is driven by two independent Brownian motions and an independent Poisson…
We consider a $N$-particle interacting particle system with the vision geometrical constraints and reflected noises, proposed as a model for collective behavior of individuals. We rigorously derive a continuity-type of mean-field equation…
We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical…
High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points…
In this paper Gaussian models of retarded and accelerated anomalous diffusion are considered. Stochastic differential equations of fractional order driven by single or multiple fractional Gaussian noise terms are introduced to describe…
In this short article we present new results that bring about hitherto unknown relations between certain Bernstein diffusions wandering in bounded convex domains of Euclidean space on the one hand, and processes which typically occur in…
We first state a special type of It\^o formula involving stochastic integrals of both standard and fractional Brownian motions. Then we use Doss-Sussman transformation to establish the link between backward doubly stochastic differential…
In this paper we first study the penalization approximation of stochastic differential equations reflected in a domain which satisfies conditions (A) and (B) and prove that the sequence of solutions of the penalizing equations converges in…
This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of…
Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be…
Stochastic variational inequalities provide a unified treatment for stochastic differential equations living in a closed domain with normal reflection and (or) singular repellent drift. When the domain is a polyhedron, we prove that the…
We study a system of Forward-Backward Stochastic Differential Equations (FBSDEs) with time-delayed generators. The forward process includes a reflection component expressed via a Stieltjes integral, while the backward process takes the form…
A representation formula for solutions of stochastic partial differential equations with Dirichlet boundary conditions is proved. The scope of our setting is wide enough to cover the general situation when the backward characteristics that…
This work is concerned with model reduction of stochastic differential equations and builds on the idea of replacing drift and noise coefficients of preselected relevant, e.g. slow variables by their conditional expectations. We extend…
In this paper, we study the reflected backward stochastic differential equations driven by G-Brownian motion with two reflecting obstacles, which means that the solution lies between two prescribed processes. A new kind of approximate…
The convergence to the stationary regime is studied for Stochastic Differential Equations driven by an additive Gaussian noise and evolving in a semi-contractive environment, i.e. when the drift is only contractive out of a compact set but…
In this paper we consider stochastic Fokker-Planck Partial Differential Equations (PDEs), obtained as the mean-field limit of weakly interacting particle systems subjected to both independent (or idiosyncratic) and common Brownian noises.…
We consider a stochastic partial differential equation with logarithmic (or negative power) nonlinearity, with one reflection at 0 and with a constraint of conservation of the space average. The equation, driven by the derivative in space…