An Introduction to Continuous Markov Processes

Doctor Daniel Gillespie, Naval Air Warfare Center, Computational Sciences Division of the Research and Technology Department

"Continuous Markov processes" can be viewed as stochastic generalizations of the deterministic functions of time that arise in physical applications of ordinary calculus. The venerable physical phenomena of Brownian motion and Johnson noise find their most natural mathematical descriptions in terms of continuous Markov process theory, as does also the more recently discovered phenomenon of stochastic resonance. This talk will introduce, at an elementary-level, the key elements of continuous Markov process theory. Topics discussed will be the Langevin equation, Gaussian white noise, the Fokker-Planck equation, Brownian motion, Johnson noise, and Monte Carlo simulation.