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Baldi P., Mazliak L., Priouret P. — Martingales and Markov Chains: Solved Exercises and Elements of Theory
Baldi P., Mazliak L., Priouret P. — Martingales and Markov Chains: Solved Exercises and Elements of Theory

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Название: Martingales and Markov Chains: Solved Exercises and Elements of Theory

Авторы: Baldi P., Mazliak L., Priouret P.


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: en

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

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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 $\mathbb{Z}$      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 $\mathbb{Z}$      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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