Reversibility and Stochastic Networks
by F.P. Kelly
Publisher: John Wiley and Sons Ltd 1979
Number of pages: 233
Examines the behavior in equilibrium of vector stochastic processes or stochastic networks, considering a wide range of applications by discussing stochastic models that arise in fields such as operational research, biology, and polymer science. Reviews the concept of reversibility, including material necessary to establish terminology and notation. Explains such uses as the study of the output from a queue, the flow of current in a conductor, the age of an allele, and the equilibrium distribution of a polymerization process. Also examines the extent to which the assumption of reversibility can be relaxed without destroying the associated tractability. Requires an understanding of Markov processes.
Home page url
Download or read it online for free here:
by S.P. Meyn, R.L. Tweedie - Springer
The book on the theory of general state space Markov chains, and its application to time series analysis, operations research and systems and control theory. An advanced graduate text and a monograph treating the stability of Markov chains.
by H. Kunita - Tata Institute Of Fundamental Research
The author presents basic properties of stochastic flows, specially of Brownian flows and their relations with local characteristics and with stochastic differential equations. Various limit theorems for stochastic flows are presented.
by M. Gubinelli, N. Perkowski - arXiv
The aim is to introduce the basic problems of non-linear PDEs with stochastic and irregular terms. We explain how it is possible to handle them using two main techniques: the notion of energy solutions and that of paracontrolled distributions.
by Alan Bain
An informal introduction to Stochastic Calculus, and especially to the Ito integral and some of its applications. The text concentrates on the parts of the course which the author found hard, there is little or no comment on more standard matters.