Conditional Markov processes and Their Application to the Theory of Optimal Control
By: by R.L. Stratonovich. Translated from the Russian by R.N. and N.B. McDonough, for Scripta Technica. With a pref. by Richard Bellman.
Edition: Second edition
Series: Modern analytic and computational methods in science and mathematics
Publisher: American Elsevier Pub. Co.; AMERICAN ELSEVIER PUBL CO
Published: 1968
Place of publication: New York
Language: eng
Translated from: rus
Translation of: Uslovnye markovskie prot͡s︡essy
Format: Hardcover
Number of pages: 370
ISBN-13: 9780444000279
Copyright date: ©1968
Subjects: Markov processes.; Control theory.
Other titles: Uslovnye markovskie prot͡s︡essy
Description: Using   this  description  the  statex(j,  w) of the system and the (noisy) observation y{j, w) of thestate  are Markov  Processes.   The basic  problem  in  optimalfiltering becomes  the derivation  of  equations  describing theevolution  of the probability  distribution  of x(j)  conditionalin  the available  observations y{j), re[t0,  t], or the evolutionof some risk function determined  by the posterior distribution.The  optimal  control  problem  becomes  the determination  ofa  realisable  control  (function  of t and the available  observa-tions)  to  minimise  an  expected   risk.   To  deal  rigorouslywith   these  continuous-time   conditional   Markov   processesrequires  the development  of mathematical  tools  of the samekind  as those available for Markov  processes, and this is oneof  the main  intentions  of the present  volume.
Notes: Bibliography: p. 342-347.
An expanded and amended version of the original Russian ed., made by the author.
Translation of [Uslovnye markovskie prot͡s︡essy]
Table of contents: title: ◙ Part I : Some Auxiliary Questions In The Theory Of Markov Processes; title: - The Convergence of Non-Markov to Markov Processes; title: - A new form of presentation of Stochastic Integrals and Equations; title: - Markov Measures and Infinitesimal Operators; title: - Absolute Continuity of Diffusional Markov Measures and Derivatives in Function Space; title: ◙ Part II : The Main Results Of The Theory Of Conditional Markov-Processes; title: - Some general results for processes in an Arbitrary Phase Space; title: - Discontinuous changes of an Observed Diffusion Process; title: - Incomplete observation of a Multidimensional Diffusion Process; title: ◙ Part III : Application Of The Theory Of Conditional Markov Processes To The Theory Of Optimal Control; title: - Some general results of the Theory of Optimal Control; title: - Optimal Nonlinear Filtering; title: - Problems of Optimal Process Termination; title: - Selection of Optimal Observation and Optimal Control of The Process; title: - Appendix I; title: - Appendix II; title: - Supplement; title: - References; title: - Index