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Markov Chains
ISBN-13:
9781475731248
Veröffentl:
2013
Seiten:
444
Autor:
Pierre Bremaud
Serie:
31, Texts in Applied Mathematics
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. However it is motivated by significant applications and progressively brings the student to the borders of contemporary research. Examples are from a wide range of domains, including operations research and electrical engineering. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.
1 Probability Review.- 2 Discrete-Time Markov Models.- 3 Recurrence and Ergodicity.- 4 Long Run Behavior.- 5 Lyapunov Functions and Martingales.- 6 Eigenvalues and Nonhomogeneous Markov Chains.- 7 Gibbs Fields and Monte Carlo Simulation.- 8 Continuous-Time Markov Models.- 9 Poisson Calculus and Queues.- 1 Number Theory and Calculus.- 1.1 Greatest Common Divisor.- 1.2 Abel's Theorem.- 1.3 Lebesgue's Theorems for Series.- 1.4 Infinite Products.- 1.5 Tychonov's Theorem.- 1.6 Subadditive Functions.- 2 Linear Algebra.- 2.1 Eigenvalues and Eigenvectors.- 2.2 Exponential of a Matrix.- 2.3 Gershgorin's Bound.- 3 Probability.- 3.1 Expectation Revisited.- 3.2 Lebesgue's Theorems for Expectation.- Author Index.
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