Markov processes and kinetic equations ( last chapter final draft )

Quantification of heart rate variability by discrete nonstationary non-Markov stochastic processes.

We develop the statistical theory of discrete nonstationary non-Markov random processes in complex systems. The objective of this paper is to find the chain of finite-difference non-Markov kinetic equations for time correlation functions (TCF) in terms of nonstationary effects. The developed theory starts from careful analysis of time correlation through nonstationary dynamics of vectors of ini...

Nonlinear Markov processes and kinetic equations

Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes

The nonlinear Markov processes are measure-valued dynamical systems which preserve positivity. They can be represented as the law of large numbers limits of general Markov models of interacting particles. In physics, the kinetic equations allow Lyapunov functionals (entropy, free energy, etc.). This may be considered as a sort of inheritance of the Lyapunov functionals from the microscopic mast...

An Introduction to Stochastic Epidemic Models

A brief introduction to the formulation of various types of stochastic epidemic models is presented based on the well-known deterministic SIS and SIR epidemic models. Three different types of stochastic model formulations are discussed: discrete time Markov chain, continuous time Markov chain and stochastic differential equations. Properties unique to the stochastic models are presented: probab...

A Quick Introduction to Kinetic Theory

The purpose of these notes is to advertise kinetic theory to beginning graduate students with an interest in analysis and differential equations. Kinetic theory is a very active area of research in mathematics, yet there are few introductory expositions to the field. These notes provide an overview of some fundamental examples in kinetic theory, while including sufficient detail to make it appa...