Related papers: Mean-field backward stochastic differential equati…
We study optimal control for mean-field forward backward stochastic differential equations with payoff functionals of mean-field type. Sufficient and necessary optimality conditions in terms of a stochastic maximum principle are derived. As…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization…
In this paper, we investigate mean-field backward stochastic differential equation (MFBSDE) with double mean reflections and nonlinear resistance. Specifically, the constraints are formulated in terms of the expectation of the solution, and…
We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.
Multiscale analysis of a degenerate pseudoparabolic variational inequality, modelling the two-phase flow with dynamical capillary pressure in a perforated domain, is the main topic of this work. Regularisation and penalty operator methods…
We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference…
In this work and the supporting Part II, we examine the performance of stochastic sub-gradient learning strategies under weaker conditions than usually considered in the literature. The new conditions are shown to be automatically satisfied…
In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…
In this paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the convergence which leads, for smooth problems, to the ODE…
Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the equation can be degenerate. Some generalized solutions…
The classical Hormander's inequality for linear partial differential operators with constant coeffcients is extended to pseudodifferential operators.
In this paper, we consider the backward stochastic differential equation (BSDE) with generator $f(y)|z|^2,$ where the function $f$ is defined on an open interval $D$ and locally integrable. The existence and uniqueness of bounded solutions…
We study the existence and uniqueness of the solution for the following backward stochastic variational inequality with oblique reflection (for short, $BSVI\left(H(t,y),\varphi,F\right)$), written under differential form \[…
In this paper we consider a mean-field backward stochastic differential equation (BSDE) driven by a Brownian motion and an independent Poisson random measure. Translating the splitting method introduced by Buckdahn, Li, Peng and Rainer [6]…
We study stochastic differential equations with jumps with no diffusion part. We provide some basic stochastic characterizations of solutions of the corresponding non-local partial differential equations and prove the Harnack inequality for…
We examine existence and uniqueness of strong solutions of multi-dimensional mean-field stochastic differential equations with irregular drift coefficients. Furthermore, we establish Malliavin differentiability of the solution and show…
We define, in a consistent way, non-local pseudo-differential operators acting on a space of analytic functionals. These operators include the fractional derivative case. In this context we show how to solve homogeneous and inhomogeneous…
This work focuses on the mean field stochastic partial differential equations with nonlinear kernels. We first prove the existence and uniqueness of strong and weak solutions for mean field stochastic partial differential equations in the…