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MILITARY OPERATIONS RESEARCH: Quantitative Decision Making -- Copyright -- CONTENTS -- PREFACE -- ACKNOWLEDGMENTS -- 1 OPERATIONS RESEARCH IN DEFENSE -- 2 SEARCH, DETECTION AND DAMAGE ASSESSMENT -- 3 SIMULATION OF MILITARY SYSTEMS -- 4 WAR GAMES -- 5 COST EFFECTIVENESS ANALYSIS -- 6 OPTIMIZATION PROBLEMS -- 7 HEURISTIC OPTIMIZATION -- 8 THE ANALYTIC HIERARCHY PROCESS -- 9 HOMOGENEOUS COMBAT MODELS -- 10 HETEROGENEOUS COMBAT MODELS -- 11 THREAT ASSESSMENT : STATIC AND DYNAMIC ANALYSES -- 12 ANALYSIS OF STRATEGIC STABILITY ISSUES -- AUTHOR INDEX -- SUBJECT INDEX.

AbstractThe effects of environmental stochasticity in a Lanchester‐type model of combat are investigated. The methodology is based on a study of stochastic differential equations with random parameters characterized by dichotomous Markov processes. Exact expressions for the Laplace transforms of the time evolution of the first‐ and second‐order moments of the system are obtained. A special case when the fluctuations in the parameters occur with great rapidity in comparison with the natural time scale of the system is also analyzed. The stochastic stability in the mean‐square sense is discussed by using the Routh–Hurwitz criterion and it is found that the stochastic perturbations tend to destabilize the system.