In this paper, existence, uniqueness and continuity of the adapted solutions for neutral stochastic delay Volterra equations with singular kernels are discussed. In addition, continuous dependence on the initial date is also investigated. Finally, stochastic Volterra equation with the kernel of fractional Brownian motion is studied to illustrate the effectiveness of our results.

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 7 November 2019Accepted: 02 February 2021Published online: 20 April 2021Keywordsinfinite-dimensional Lyapunov equation, integral operator Riccati linear-quadratic control, stochastic Volterra equationsAMS Subject Headings47G10, 49N10, 34G20Publication DataISSN (print): 03...

In this paper, an iterative scheme for extracting approximate solutions of two dimensional Volterra-Fredholm integral equations is proposed. Considering some conditions on the kernel of the integral equation obtained by discretization of the integral equation, the convergence of the approximate solution to the exact solution is investigated. Several examples are provided to demonstrate the effi...

‎in this paper‎, ‎we construct a new iterative method for solving nonlinear volterra integral equation of second kind‎, ‎by approximating the legendre polynomial basis‎. ‎error analysis is worked using banach fixed point theorem‎. ‎we compute the approximate solution without using numerical method‎. ‎finally‎, ‎some examples are given to compare the results with some of the existing methods‎.

in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

The first passage time problem for Brownian motions hitting a barrier has been extensively studied in the literature. In particular, many incarnations of integral equations which link the density of the hitting time to the equation for the barrier itself have appeared. Most interestingly, Peskir (2002b) demonstrates that a master integral equation can be used to generate a countable number of n...

We extend recent results on affine Volterra processes to the inhomogeneous case. This includes moment bounds of solutions equations driven by a Brownian motion with an kernel K(t,s) and drift diffusion coefficients b(s,Xs) σ(s,Xs). In case b σσT we show how conditional Fourier–Laplace functional can be represented solution Riccati–Volterra integral equation. For convolution type K(t,s)=K¯(t−s) ...