Related papers: Martingale Problem under Nonlinear Expectations

This article studies the Cauchy problem for the Boltzmann equation with stochastic kinetic transport. Under a cut-off assumption on the collision kernel and a coloring hypothesis for the noise coefficients, we prove the global existence of…

By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions…

Sufficient conditions for the invariance of evolution problems governed by perturbations of (possibly nonlinear) $m$-accretive operators are provided. The conditions for the invariance with respect to sublevel sets of a constraint…

The work concerns nonlinear filtering problems of stochastic differential equations with correlated L\'evy noises. First, we establish the Kushner-Stratonovich and Zakai equations through martingale representation theorems and the…

We consider a viscous incompressible fluid interacting with a linearly elastic shell of Koiter type which is located at some part of the boundary. Recently models with stochastic perturbation in the shell equation have been proposed in the…

In this paper we study a nonlinear stochastic fluid-structure interaction problem with a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a…

The paper is concerned with a McKean-Vlasov type SDE with drift in anisotropic Besov spaces with negative regularity and with degenerate diffusion matrix under the weak H{\"o}rmander condition. The main result is of existence and uniqueness…

We consider a Cauchy problem for the inhomogeneous differential equation given in terms of an unbounded linear operator $A$ and the Caputo fractional derivative of order $\alpha \in (0, 2)$ in time. The previously known representation of…

In this paper we consider a boundary value problem for fully fourth order nonlinear functional differential equation which contains all lower derivatives of proportional delay arguments. By the reduction of the problem to operator equation…

In this paper we introduce the concept of conic martingales}. This class refers to stochastic processes having the martingale property, but that evolve within given (possibly time-dependent) boundaries. We first review some results about…

We consider quasi-static poroelastic systems with incompressible constituents. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid…

The aim of this article is to show the global existence of both martingale and pathwise solutions of stochastic equations with a monotone operator, of the Ladyzenskaya-Smagorinsky type, driven by a general Levy noise. The classical approach…

We construct solutions to the randomly-forced Navier--Stokes--Poisson system in periodic three-dimensional domains or in the whole three-dimensional Euclidean space. These solutions are weak in the sense of PDEs and also weak in the sense…

By decoupling forward and backward stochastic trajectories, we construct a family of martingales and work theorems for both overdamped and underdamped Langevin dynamics. Our results are made possible by an alternative derivation of work…

We consider the variational wave equation in one-dimensional space with stochastic forcing by an additive noise. Blow-up of local smooth solutions is established, and global existence is proved in the class of weak martingale solutions.

The aim of this paper is to introduce a new formalism for the deterministic analysis associated with backward stochastic differential equations driven by general c{\`a}dl{\`a}g martingales. When the martingale is a standard Brownian motion,…

Developing a thermodynamic theory of computation is a challenging task at the interface of non-equilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times,…

This paper focuses on inverse problems to identify parameters by incorporating information from measurements. These generally ill-posed problems are formulated here in a probabilistic setting based on Bayes's theorem because it leads to a…

This paper is concerned with the stochastic Hamilton-Jacobi-Bellman equation with controlled leading coefficients, which is a type of fully nonlinear backward stochastic partial differential equation (BSPDE for short). In order to formulate…

We establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with estimates for the non-asymptotic rate at which the residuals vanish. Strong and…