Class Of Stochastic Functional Equations Research Articles

On a unique solution and stability analysis of a class of stochastic functional equations arising in learning theory

Abstract Numerous computational and learning theory models have been studied using probabilistic functional equations. Especially in two-choice scenarios, the vast bulk of animal behavior research divides such situations into two different events. They split these actions into two possibilities according to the animals’ progress toward a particular decision. However, reward plays a crucial role in such experiments because, based on the selected side and the food placement, such scenarios may be classified into four distinct categories. This article aims to explore the animals’ reactions to such circumstances by presenting a generic stochastic functional equation. By using the well-known fixed point theory results, we examine the existence, uniqueness, and stability of solutions to the suggested functional equation. Moreover, an example is included to emphasize the significance of our findings.

The existence and uniqueness of solution for a class of stochastic functional equations on S.R Space

This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X=ϕ˜(X), where ϕ˜:B→B and B is a Banach space consisted of all left-continuous, (Ft)-adapted processes. Also, the main result is applied to some S.D.E (or S.I.E.). And the authors adopted some of the results in current research in the models of stochastic control recently. This paper proves the existence and uniquence and uniqueness of solution for stochastic functional equation. A series of corollaries are deduced from the special examples of the theorems in this paper.