On a class of stochastic functional integral equations
On a pair of random generalized non-linear contractions.
On existence and an asymptotic behavior of random solutions of a class of stochastic functional-integral equations
On existence, uniqueness and stability of solutions of multidimensional SDE's with reflecting boundary conditions
On filtering over Îto-Volterra observations.
On Fredholm integral equations with random degenerate kernels
On one-dimensional diffusion processes living in a bounded space interval
We prove that under some assumptions a one-dimensional Itô equation has a strong solution concentrated on a finite spatial interval, and the pathwise uniqueness holds.
On solutions of general nonlinear stochastic integral equations.
On solutions set of a multivalued stochastic differential equation
We analyse multivalued stochastic differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued stochastic differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded.
On some fractional stochastic integrodifferential equations in Hilbert space.
On some limit theorems for solutions of stochastic differential equations
On some sample path properties of Skorohod integral processes
On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains
Let D be an open convex set in and let F be a Lipschitz operator defined on the space of adapted càdlàg processes. We show that for any adapted process H and any semimartingale Z there exists a unique strong solution of the following stochastic differential equation (SDE) with reflection on the boundary of D: , t ∈ ℝ⁺. Our proofs are based on new a priori estimates for solutions of the deterministic Skorokhod problem.
On the existence and asymptotic behavior of the random solutions of the random integral equation with advancing argument
1. Introduction Random Integral Equations play a significant role in characterizing of many biological and engineering problems [4,5,6,7]. We present here new existence theorems for a class of integral equations with advancing argument. Our method is based on the notion of a measure of noncompactness in Banach spaces and the fixed point theorem of Darbo type. We shall deal with random integral equation with advancing argument , (t,ω) ∈ R⁺ × Ω, (1) where (i) (Ω,A,P) is a complete probability space, (ii)...
On the existence and uniqueness of the solution processes in McShane's stochastic integral equation systems
On the existence, uniqueness and parametric dependence on the coefficients of the solution processes in McShane's stochastic integral equations.
In this paper we use the Schauder fixed point theorem and methods of integral inequalities in order to prove a result on the existence, uniqueness and parametric dependence on the coefficients of the solution processes in McShane stochastic integral equations.
On the positivity and zero crossings of solutions of stochastic Volterra integrodifferential equations.
On the probability model for solving some integral equations of second type
On the uniqueness of solutions of stochastic differential equations with reflecting barrier conditions
Onsager-Machlup functional for stochastic evolution equations