Markov Processes by E B Dynkin

Markov Processes by E B Dynkin

The modem theory of Markov processes has its origins in the studies of A. A. MARKOV (1906-1907) on sequences of experiments connected in a chain and in the attempts to describe mathematically the physical phenomenon known as Brownian motion (L. BACHELlER 1900, A. EIN- STEIN 1905). The first correct mathematical construction of a Markov process with continuous trajectories was given by N. WIENER in 1923. (This process is often called the Wiener process.) The general theory of Markov processes was developed in the 1930's and 1940's by A. N. KOL- MOGOROV, W. FELER, W. DOEBLlN, P. LEVY, J. L. DOB, and others. During the past ten years the theory of Markov processes has entered a new period of intensive development. The methods of the theory of semigroups of linear operators made possible further progress in the classification of Markov processes by their infinitesimal characteristics. The broad classes of Markov processes with continuous trajectories be- came the main object of study. The connections between Markov pro- cesses and classical analysis were further developed. It has become possible not only to apply the results and methods of analysis to the problems of probability theory, but also to investigate analytic problems using probabilistic methods. Remarkable new connections between Markov processes and potential theory were revealed. The foundations of the theory were reviewed critically: the new concept of strong Markov process acquired for the whole theory of Markov processes great importance.

SKU	Unavailable
ISBN 13	9783662000335
ISBN 10	3662000334
Title	Markov Processes
Author	E B Dynkin
Series	Grundlehren Der Mathematischen Wissenschaften
Condition	Unavailable
Binding Type	Paperback
Publisher	Springer
Year published	2012-08-01
Number of pages	366
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable