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Baldi P., Mazliak L., Priouret P. — Martingales and Markov Chains: Solved Exercises and Elements of Theory
 Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter Название: Martingales and Markov Chains: Solved Exercises and Elements of Theory Авторы: Baldi P., Mazliak L., Priouret P. Аннотация: A thorough grounding in Markov chains and martingales is essential in dealing with many problems in applied probability, and is a gateway to the more complex situations encountered in the study of stochastic processes. Exercises are a fundamental and valuable training tool that deepen students' understanding of theoretical principles and prepare them to tackle real problems.In addition to a quick but thorough exposition of the theory, Martingales and Markov Chains: Solved Exercises and Elements of Theory presents, more than 100 exercises related to martingales and Markov chains with a countable state space, each with a full and detailed solution. The authors begin with a review of the basic notions of conditional expectations and stochastic processes, then set the stage for each set of exercises by recalling the relevant elements of the theory. The exercises range in difficulty from the elementary, requiring use of the basic theory, to the more advanced, which challenge the reader's initiative. Each section also contains a set of problems that open the door to specific applications.Designed for senior undergraduate- and graduate level students, this text goes well beyond merely offering hints for solving the exercises, but it is much more than just a solutions manual. Within its solutions, it provides frequent references to the relevant theory, proposes alternative ways of approaching the problem, and discusses and compares the arguments involved. Язык: Рубрика: Математика/ Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1998 Количество страниц: 192 Добавлена в каталог: 18.04.2010 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
Предметный указатель
 Absorbing, slate      84 Adapted, process      15 Altered probability space      15 Aperiotiicity      90 Associated increasing process      27 Barrier function criterion      112 Beppo Levi's theorem      2 Bernoulli — Laplace diffusion      101 Borel — Cantelli lemma      35 Canonical space      16 Closed class      84 Conditional expectation, t      2 Conditional law      1 4 Conditional law of Gaussian vectors      6 Coupling      115 Dcob's inequality      26 Detailed balance equation      91 Doob's decomposition      24 Dynkin's criterion      103 Ehienfesi. model      95 Equi-integrability      39 Ergodic theorem      88 Excessive, function      79 Excessive, measure      79 Fatou’s iemma      2 Filtration      15 Filtration, natural      23 73 Finite dimensional distributions      16 Foster recurrence criterion      114 Galton — Watson process      109 Harmonic, function      7 Hitting time, l      7 Increasing predictable process      24 Invariant, function      79 Invariant, measure      79 Inverse martingale      30 Irreducible      84 Jensen's inequalily      2 24 Kolmogorov's theorem      16 Krickeberg's decomposition      35 Kronecker's lemma      33 Kupermartingale      23 Lebesguc’s theorem      2 Markov chain      15 Markov chain, aperiodic      90 Markov chain, birth and death      96 100 Markov chain, bistochastic      90 Markov chain, canonical      76 Markov chain, dual      85 Markov chain, homogeneous      73 Markov chain, inhomogeneous      73 Markov chain, irreducible      84 Markov chain, null recurrent      87 Markov chain, positive recurrent      87 Markov chain, product      106 Markov chain, recurrent      84 Markov chain, transient      84 Markov property      73 77 Markov property, strong      77 Martingale      15 23 Martingale with independent increments      3 Maximal inequalities      2 Maximum principle      82 102 Metropolis algorithm      103 Monotone class theorem      16 Natural filtration      23 73 Optimal stopping      111 Pasitive, maitingale      23 Pasitive, submarlingale      23 Pasitive, supermartingale      23 Passage lime      17 Perfect sampling      104 Period of a chain      89 Potential matrix      78 Potential of a function      79 Queueing chain      1 15 Raikm — Nikodym theoiem      41 Random walk on       116 Random walk on a graph      97 Random walk on the hypercube      103 Random walk on the vertices or a polygon      11 8 Random walk simple on       95 Recurrent, cluiin      84 Recurrent, state      82 Return time      17 Riesz decomposition      10 Stationary measure      79 Stochastic process      15 Stopping theorem      24 Stopping times      17 Submartingale      23 Transient chain      84 Transient, siale      82 Transition matrix      73 Translation operator      77 Uniform integrability      39 Wald identities      37
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