Markov Processes: Characterization and Convergence
The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.
"[A]nyone who works with Markov processes whose state space is uncountably infinite will need this most impressive book as a guide and reference."
"There is no question but that space should immediately be reserved for [this] book on the library shelf. Those who aspire to mastery of the contents should also reserve a large number of long winter evenings."
-Zentralblatt für Mathematik und ihre Grenzgebiete/Mathematics Abstracts
"Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that [is] useful both as a reference work and as a graduate textbook."
-Journal of Statistical Physics
Markov Processes presents several different approaches to proving weak approximation theorems for Markov processes, emphasizing the interplay of methods of characterization and approximation. Martingale problems for general Markov processes are systematically developed for the first time in book form. Useful to the professional as a reference and suitable for the graduate student as a text, this volume features a table of the interdependencies among the theorems, an extensive bibliography, and end-of-chapter problems.
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8 Examples of Generators
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apply approximation assume Borel measurable bounded linear operator Brownian motion Chapter closure compact set complete and separable Consequently continuous contraction semigroup converges in distribution Corollary Let countable deﬁne deﬁnition denote dense dissipative Feller semigroup ﬁltration ﬁnd ﬁnite ﬁrst ﬁxed given hence holds implies independent inequality initial distribution Kurtz lemma Let Let f lim sup locally compact Markov chain Markov process Markov process corresponding martingale problem metric space modiﬁcation nonanticipating solution nonnegative Note paths in DE[0 Poisson process probability space processes with sample Proposition Let random variables real-valued relatively compact result right continuous sample paths satisﬁes satisfying Section semigroup on C(E semigroup T(t sequence Show single-valued stationary distribution Statistical stochastic process strongly continuous contraction submartingale subset subspace Suppose Theorem 4.1 Theorem Let transition function uniqueness well-posed zero