Related papers: Support theorem for stochastic variational inequal…

The work concerns invariant measures for multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the exponential ergodicity of these equations. Then for a sequence of these equations, when their coefficients…

We consider the Stokes phenomenon for the solutions of some partial differential equations with variable coefficients in two complex variables, where initial data are holomorphic. We use the theory of (moment) summability and the theory of…

We study nested variational inequalities, which are variational inequalities whose feasible set is the solution set of another variational inequality. We present a projected averaging Tikhonov algorithm requiring the weakest conditions in…

Variational inequalities are a universal optimization paradigm that is interesting in itself, but also incorporates classical minimization and saddle point problems. Modern realities encourage to consider stochastic formulations of…

We study the stochastic nonlinear Schroedinger equations with linear multiplicative noise, particularly in the defocusing mass-critical and energy-critical cases. For general initial data, we prove the global existence and uniqueness of…

By the methods of probability and duality technique, we give some comparison theorems for the solutions of infinite horizon forward-backwad stochastic differential equations.

Some little considerations concerning the application of the Theory of Dirichlet Forms to stocastic variational principle on riemannian manifolds are performed

We prove the Yamada-Watanabe Theorem for semilinear stochastic partial differential equations with path-dependent coefficients. The so-called "method of the moving frame" allows us to reduce the proof to the Yamada-Watanabe Theorem for…

The purpose of this paper is to establish the theory of stochastic pseudo-differential operators and give its applications in stochastic partial differential equations. First, we introduce some concepts on stochastic pseudo-differential…

In this paper, we characterize the topological support in Holder norm of the law of the solution to a stochastic wave equation with three-dimensional space variable is proved. This note is a continuation of [9] and [10]. The result is a…

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an…

In this Note, we present a Calder\'on-type uniqueness theorem on the Cauchy problem of stochastic partial differential equations. To this aim, we introduce the concept of stochastic pseudo-differential operators, and establish their…

One standard way to prove existence for deterministic, highly nonlinear PDEs is to use the Schauder-Tychonoff fixed-point theorem. In what follows, we introduce and verify a stochastic variant of the Schauder-Tychonoff theorem. We apply our…

A variational approach is presented to calculate the stress field generated by a system of dislocations. It is shown that in the simplest case, when the material containing the dislocations obeys Hooke's law the variational framework gives…

Our aim in this paper is to establish some strong stability properties of a solution of a stochastic differential equation driven by a fractional Brownian motion for which the pathwise uniqueness holds. The results are obtained using…

This paper studies a non-stochastic version of Fernholz's stochastic portfolio theory for a simple model of stock markets with continuous price paths. It establishes non-stochastic versions of the most basic results of stochastic portfolio…

We prove variational forms of the Barban-Davenport-Halberstam Theorem and the large sieve inequality. We apply our result to prove an estimate for the sum of the squares of prime differences, averaged over arithmetic progressions.

We study the invariance of stochastic differential equations under random diffeomorphisms, and establish the determining equations for random Lie-point symmetries of stochastic differential equations, both in Ito and in Stratonovich form.…

The concept of nonlinear split ordered variational inequality problems on partially ordered vector spaces is a natural extension of linear split vector variational inequality problems on Banach spaces. The results about nonlinear split…

This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under nonholonomic constraints. For this…