Research for Stochastic Processes

A model that characterizes an air-to-air engagement as a semi-Markov process is described. Included is a discussion of the model's assumptions and effectiveness measures with instructions for applying the model to experiments characterizing offensive and defensive maneuvering capability in air combat.

This study describes two stochastic models for evaluating air combat maneuvering (ACM) engagements. The Maneuver Conversion Model is applicable to engagements where a successful outcome is determined primarily by maneuvering effectiveness of the combatants. In this model, the events of air-to-air engagements are assumed to behave as a semi-Markov process with various absorbing states. The Firing Sequence Model is intended for analysis of engagements where a successful outcome depends on aircrew ability to capitalize on weapon performance. This model also assumes a Markov process, but analyzes test-range data as tabulations of weapon-firing incidents for each engagement. Common measures of effectiveness, such as the probability of achieving first weapon-firing opportunity and the expected exchange ratio, may be used in both models to estimate ACM performance. Volume I presents the analytic methodologies for both models, and provides under CNO Project P/V2 (Battle Cry), and illustrates the Maneuver Conversion Model methodology.

In this paper, a path-integral representation is constructed for propagators corresponding to quantum Hamiltonian operators obtained from classical Hamiltonians by an arbitrary rule of correspondence. Each rule yields a unique way of defining the path integral in the context of a formalism which does not require a limiting process. This formalism is more reliable than the usual lattice definition in that all the expressions it entails are well-defined for computational purposes and it allows the explicit evaluation of large classes of path integrals. Direct substitution in the Schrodinger equation shows that there are no restrictions on the Hamiltonian operator. Examples are given.

The exact distribution is given for the number of times the vertical steps of an empirical distribution cross the underlying theoretical distribution. The statistic was used for Smirnov [1] to derive limiting distributions of statistics used in Kolmogorov-Smirnov tests, and may be used as a goodness-of-fit test in its own right.