000 02928nam a22004575i 4500
001 978-3-540-26990-8
003 DE-He213
005 20161121230932.0
007 cr nn 008mamaa
008 100301s2005 gw | s |||| 0|eng d
020 _a9783540269908
_9978-3-540-26990-8
024 7 _a10.1007/b138428
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aStroock, Daniel W.
_eauthor.
245 1 3 _aAn Introduction to Markov Processes
_h[electronic resource] /
_cby Daniel W. Stroock.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2005.
300 _aXIV, 178 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v230
505 0 _aRandom Walks A Good Place to Begin -- Doeblin's Theory for Markov Chains -- More about the Ergodic Theory of Markov Chains -- Markov Processes in Continuous Time -- Reversible Markov Processes -- Some Mild Measure Theory.
520 _aTo some extent, it would be accurate to summarize the contents of this book as an intolerably protracted description of what happens when either one raises a transition probability matrix P (i. e. , all entries (P)»j are n- negative and each row of P sums to 1) to higher and higher powers or one exponentiates R(P — I), where R is a diagonal matrix with non-negative entries. Indeed, when it comes right down to it, that is all that is done in this book. However, I, and others of my ilk, would take offense at such a dismissive characterization of the theory of Markov chains and processes with values in a countable state space, and a primary goal of mine in writing this book was to convince its readers that our offense would be warranted. The reason why I, and others of my persuasion, refuse to consider the theory here as no more than a subset of matrix theory is that to do so is to ignore the pervasive role that probability plays throughout. Namely, probability theory provides a model which both motivates and provides a context for what we are doing with these matrices. To wit, even the term "transition probability matrix" lends meaning to an otherwise rather peculiar set of hypotheses to make about a matrix.
650 0 _aMathematics.
650 0 _aProbabilities.
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540234999
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v230
856 4 0 _uhttp://dx.doi.org/10.1007/b138428
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c506129
_d506129