Related papers: Multivalued stochastic Dirichlet-Neumann problems …
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
A classification theorem for linear differential equations in two variables (one real and one Grassmann) having polynomial solutions(the generalized Bochner problem) is given. The main result is based on the consideration of the eigenvalue…
The stochastic gradient descent has been widely used for solving composite optimization problems in big data analyses. Many algorithms and convergence properties have been developed. The composite functions were convex primarily and…
In this paper, we generalize the classical Yosida approximation by utilizing a nonstandard duality mapping to establish the existence and uniqueness of both (probabilistically) weak and strong solutions and demonstrate the continuous…
In this Note, assuming that the generator is uniform Lipschitz in the unknown variables, we relate the solution of a one dimensional backward stochastic differential equation with the value process of a stochastic differential game. Under a…
The main result establishes the existence of a solution in a generalized sense for a nonlinear Dirichlet problem driven by a competing operator and exhibiting a convection term composed with an intrinsic operator. A finite dimensional…
In this paper, we study a class of multi-dimensional reflected backward stochastic differential equations when the noise is driven by a Brownian motion and an independent Poisson point process, and when the solution is forced to stay in a…
In this paper, we study reflected generalized backward doubly stochastic differential equations driven by Teugels martingales associated with L\'evy process (RGBDSDELs, in short) with one continuous barrier. Under uniformly Lipschitz…
We generalize the Donsker-Varadhan minimax formula for the principal eigenvalue of a uniformly elliptic operator in nondivergence form to the first principal half-eigenvalue of a fully nonlinear operator which is concave (or convex) and…
In the present paper we introduce a concept of doubly stochastic quadratic operator. We prove necessary and sufficient conditions for doubly stochasticity of operator. Besides, we prove that the set of all doubly stochastic operators forms…
In this paper we investigate the sensitivity analysis of parameterized nonlinear variational inequalities of second kind in a Hilbert space. The challenge of the present work is to take into account a perturbation on all the data of the…
In this paper, a class of reflected generalized backward doubly stochastic differential equations (reflected GBDSDEs in short) driven by Teugels martingales associated with L\'{e}vy process and the integral with respect to an adapted…
We consider the large sum of DC (Difference of Convex) functions minimization problem which appear in several different areas, especially in stochastic optimization and machine learning. Two DCA (DC Algorithm) based algorithms are proposed:…
Backward stochastic partial differential equations of parabolic type with variable coefficients are considered in smooth domains. Existence and uniqueness results are given in weighted Sobolev spaces allowing the derivatives of the…
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…
In this paper, we are concerned with backward doubly stochastic differential evolutionary systems (BDSDESs for short). By using a variational approach based on the monotone operator theory, we prove the existence and uniqueness of the…
This work contributes a systematic survey and complementary insights of reflecting Brownian motion and its properties. Extension of the Skorohod problem's solution to more general cases is investigated, based on which a discussion is…
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 paper presents a set of complete solutions of a nonconvex variational problem with a double-well potential. Based on the canonical duality-triality theory, the associated nonlinear differential equation with either Dirichlet/Neumann or…
This book aims to provide a brief overview of recent advancements in the theory of inverse problems for stochastic partial differential equations. In order to keep the content concise, we will only discuss the inverse problems of two…