Related papers: Boundary value problems for functionals of Ito pro…
Regularity of solutions is studied for backward stochastic parabolic Ito equations. An analog of the second energy inequality and the related existence theorem are obtained for domains with boundary.
The representation theorem is obtained for functionals of non-Markov processes and their first exit times from bounded domains. These functionals are represented via solutions of backward parabolic Ito equations. As an example of…
We study linear backward stochastic partial differential equations of parabolic type with special boundary condition that connect the terminal value of the solution with a functional over the entire past solution. Uniqueness, solvability…
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…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
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.
We study existence, uniqueness, semi-group property, and a priori estimates for solutions for backward parabolic Ito equations in domains with boundary. We study also duality between forward and backward equations. The semi-group for…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
We study linear stochastic partial differential equations of parabolic type. We consider a new boundary value problem where a Cauchy condition is replaced by a prescribed average of the solution either over time and probabilistic space for…
In this paper a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for…
We consider existence of periodic boundary value problems of nonlinear second order ordinary differential equations. Under certain half Lipschitzian type conditions several existence results are obtained. As applications positive periodic…
Necessary and sufficient conditions for the solvability of boundary value problems for a family of functional differential equations with a non-integrable singularity are obtained.
Moving boundary problems allow to model systems with phase transition at an inner boundary. Driven by problems in economics and finance, in particular modeling of limit order books, we consider a stochastic and non-linear extension of the…
We study linear stochastic partial differential equations of parabolic type with non-local in time or mixed in time boundary conditions. The standard Cauchy condition at the terminal time is replaced by a condition that mixes the random…
The potential applications of boundary functionals of random processes, such as the extreme values of these processes, the moment of first reaching a fixed level, the value of the process at the moment of reaching the level, the moment of…
Using results from our companion article [arXiv:1112.4824v2] on a Schauder approach to existence of solutions to a degenerate-parabolic partial differential equation, we solve three intertwined problems, motivated by probability theory and…
The aim of this paper is to study, in the infinite dimensional framework, the existence and uniqueness for the solution of the following multivalued generalized backward stochastic differential equation, considered on a random, possibly…
Construction of splitting-step methods and properties of related non-negativity and boundary preserving numerical algorithms for solving stochastic differential equations (SDEs) of Ito-type are discussed. We present convergence proofs for a…
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…
We demonstrate that backward stochastic differential equations (BSDE) may be reformulated as ordinary functional differential equations on certain path spaces. In this framework, neither It\^{o}'s integrals nor martingale representation…