Research for Stochastic Processes

Survival curves for NPS male recruits were estimated through eight years of service using the FY 1979 cross-sectional data base. Separate analyses were performed for Class A school attendees and non-A school attendees, holding constant the effects of age, educational level, and mental group. Mean survival times (the areas under the survival curves) were calculated for each recruit profile. A cost-benefit analysis was then performed on the mean survival times calculated over four years of service to determine optimal qualifying scores for enlistment.

This paper provides a treatment of molecule-ion molecule reactions based on stochastic mechanics. Stochastic mechanics is a semi-classical theory in which one assumes that particles move as a stochastic diffusion process. It is shown that the reaction probability and reaction rate can be determined from the solution of certain Partial Differential Equations (PDE). Asymptotic solutions of these PDE are constructed in terms of incomplete special functions. The results derived using stochastic mechanics are compared with results derived using other semi-classical approximations.

A generalized critical point is characterized by totally non-linear dynamics. The deterministic and stochastic theory of relaxation is formulated at such a point. Canonical problems are used to motivate the general solutions. In the deterministic theory, it is shown that at the critical point certain modes have polynomial (rather than exponential) growth or decay. The stochastic relaxation rates can be calculated in terms of various incomplete special functions. First, a substrate inhibited reaction (marginal type dynamical system). Second, the relaxation of a mean field ferromagnet. Third, the relaxation of a critical harmonic oscillator is considered.

This paper extends a Bayesian approach to the classical methods for solving the position-finding problem.