相关论文: Linear stochastic differential equations with func…

We consider one-dimensional stochastic differential equations with a boundary condition, driven by a Poisson process. We study existence and uniqueness of solutions and the absolute continuity of the law of the solution. In the case when…

In the present paper, we give some examples of stochastic differential equations which have delicateness in the Markov and strong Markov properties, the uniqueness locally in time and globally in time, and initial conditions. Moreover, we…

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…

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.

We consider backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We show that appropriate solutions exist for arbitrary terminal conditions, and are unique up to sets of measure zero. We…

We study (backward) stochastic differential equations with noise coming from a finite state Markov chain. We show that, for the solutions of these equations to be `Markovian', in the sense that they are deterministic functions of the state…

We study function-valued solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable parabolicity hypotheses. We provide…

In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…

Boundary value problems for linear stationary dispersive equations of order $2l+1$, $l\in \mathbb{N}$ have been considered on finite intervals $(0,L)$. The existence and uniqueness of regular solutions have been established for general…

We are concerned with the solvability of linear second order elliptic partial differential equations with nonlinear boundary conditions at resonance, in which the nonlinear boundary conditions perturbation is not necessarily required to…

Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…

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…

In this note we review recent results on existence and uniqueness of solutions of infinite-dimensional stochastic differential equations describing interacting Brownian motions on $\R^d$.

We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…

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…

A non-linear differential equation arising from a stochastic process known as branching Brownian motion is considered. We find an explicit solution and show the uniqueness of the solution under some boundedness conditions using…

A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…

We consider boundary value problems for stochastic differential equations of second order with a small parameter. For this case we prove a special existence and unicity theorem for strong solutions. The asymptotic behavior of these…

This note is concerned with an important for modelling question of existence of solutions of stochastic partial differential equations as proper stochastic processes, rather than processes in the generalized sense. We consider a first order…

Let $k$ be a differential field of characteristic zero with an algebraically closed field of constants. In this article, we provide a classification of first order differential equations over $k$ and study the algebraic dependence of…