Discrete Operational Calculus in Delayed Stochastic Games

TL;DR

This paper develops an analytical framework for delayed stochastic games involving hostile processes, focusing on first passage times and casualties, and validates the formulas through various transforms.

Contribution

It introduces a novel application of discrete operational calculus to analyze delayed stochastic games with hostile processes.

Findings

Analytic formulas for first passage times are validated.

Transform methods confirm the tractability of the formulas.

The approach enhances understanding of casualties in stochastic games.

Abstract

This article deals with classes of antagonistic games with two players. A game is specified in terms of two `hostile' stochastic processes representing mutual attacks upon random times exerting casualties of random magnitudes. The game ends when one of the players is defeated. We target the first passage time $\tau_\rho$ of the defeat and the number of casualties to either player upon $\tau_\rho$. Here we validate our claim of analytic tractability of the general formulas obtained in [1] under various transforms.