The aim of the paper is to provide some regularity results for stochastic convolutions corresponding to stochastic Volterra equations in separable Hilbert space. We study convolutions of the form WΨ(t) := ∫ t 0 S(t − τ)Ψ(τ)dW (τ), t ≥ 0, where S(t), t ≥ 0, is so-called resolvent for Volterra equation considered,Ψ is an appropriate process and W is a cylindrical Wiener process. In the paper we e...

We propose a new method, called the textit{the weighted space method}, for the study of the generalized Hyers-Ulam-Rassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.

In this paper we consider a nonlinear two-phase Stefan problem in one-dimensional space. The problem is mapped into a nonlinear Volterra integral equation for the free boundary.

Volterra-Stieltjes integral equations have been studied in the space of continuous functions in many papers for example, (see [3]-[7]). Our aim here is to studing the existence of weak solutions to a nonlinear integral equation of Volterra-Stieltjes type in a reflexive Banach space. A special case will be considered.

Field theory tools are applied to analytically study fluctuation and correlation effects in spatially extended stochastic predator-prey systems. In the meanfield rate equation approximation, the classic Lotka–Volterra model is characterized by neutral cycles in phase space, describing undamped oscillations for both predator and prey populations. In contrast, Monte Carlo simulations for stochast...

an ecient method, based on the legendre wavelets, is proposed to solve thesecond kind fredholm and volterra integral equations of hammerstein type.the properties of legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known newton's method. examples assuring eciencyof the method and ...

In this paper we adapt Lavrent'ev method so to obtain a reconstruction procedure for the input u to a nonlinear input-output system described by a Volterra integral equation. The proof is based on a monotonicity assumption which does not imply the monotonicity of the operators appearing in the Volterra equation.

We consider a nonlinear Volterra-Fredholm integral equation NVFIE of the second kind. The Volterra kernel is time dependent, and the Fredholm kernel is position dependent. Existence and uniqueness of the solution to this equation, under certain conditions, are discussed. The block-byblock method is introduced to solve such equations numerically. Some numerical examples are given to illustrate o...

This paper presents a computational method for solving stochastic ItoVolterra integral equations. First, Haar wavelets and their properties are employed to derive a general procedure for forming the stochastic operational matrix of Haar wavelets. Then, application of this stochastic operational matrix for solving stochastic Ito-Volterra integral equations is explained. The convergence and error...