Markov Chains with Stationary Transition Probabilities - Grundlehren Der Mathematischen Wissenschaften - Kai Lai Chung - Grāmatas - Springer-Verlag Berlin and Heidelberg Gm - 9783642494086 - 1960
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Kai Lai Chung
Markov Chains with Stationary Transition Probabilities - Grundlehren Der Mathematischen Wissenschaften Softcover Reprint of the Original 1st Ed. 1960 edition

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The theory of Markov chains, although a special case of Markov processes, is here developed for its own sake and presented on its own merits. In general, the hypothesis of a denumerable state space, which is the defining hypothesis of what we call a "chain" here, generates more clear-cut questions and demands more precise and definitive an­ swers. For example, the principal limit theorem (§§ 1. 6, II. 10), still the object of research for general Markov processes, is here in its neat final form; and the strong Markov property (§ 11. 9) is here always applicable. While probability theory has advanced far enough that a degree of sophistication is needed even in the limited context of this book, it is still possible here to keep the proportion of definitions to theorems relatively low. . From the standpoint of the general theory of stochastic processes, a continuous parameter Markov chain appears to be the first essentially discontinuous process that has been studied in some detail. It is common that the sample functions of such a chain have discontinuities worse than jumps, and these baser discontinuities play a central role in the theory, of which the mystery remains to be completely unraveled. In this connection the basic concepts of separability and measurability, which are usually applied only at an early stage of the discussion to establish a certain smoothness of the sample functions, are here applied constantly as indispensable tools.

278 pages, 1 black & white illustrations, biography

Mediji Grāmatas     Paperback Book   (Grāmata ar mīksto vāku un līmēto muguru)
Izlaists 1960
ISBN13 9783642494086
Izdevēji Springer-Verlag Berlin and Heidelberg Gm
Lapas 278
Izmēri 155 × 235 × 15 mm   ·   412 g
Valoda Angļu  
Redaktors Grammel, R.
Redaktors Hirzebruch, F.
Redaktors Hopf, E.
Redaktors Maak, H.
Redaktors Magnus, W.
Redaktors Schmidt, F. K.
Redaktors Stein, K.
Redaktors Waerden, B. L. Van Der

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