On solutions of general nonlinear stochastic integral equations

On Solutions of General Nonlinear Stochastic Integral Equations

Stochastic or random integral equations are extremely important in the study of many physical phenomena in life sciences and engineering [3, 14, 16]. There are currently two basic versions of stochastic integral equations being studied by probabilists and mathematical statisticians, namely, those integral equations involving Ito-Doob type of stochastic integrals and those which can be formed as...

Exact solutions of nonlinear interval Volterra integral equations

Wilson wavelets for solving nonlinear stochastic integral equations

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

Polynomial solutions of nonlinear integral equations

We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of C. Bender and E. Ben-Naim. We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.

On the existence of continuous solutions of nonlinear integral equations

In this paper, we study the existence of continuous solutions over compact intervals of some nonlinear integral equations. A special interest is devoted to the study of the existence as well as the uniqueness of nonlinear Volterra equations. © 2004 Elsevier Ltd. All rights reserved.