Stochastic processes and models /

Provides an introduction to simple stochastic processes and models. Including numerous exercises, problems and solutions, this book covers the key concepts and tools.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Stirzaker, David
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Oxford ; New York : Oxford University Press, 2005.
Temas:
Stochastic processes.
Stochastic models.
Stochastic Processes
Processus stochastiques.
Modèles stochastiques.
MATHEMATICS > Probability & Statistics > Stochastic Processes.
Mathematics.
Stochastischer Prozess
Stochastische processen.
Markov-processen.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro; Contents; Preface; 1 Probability and random variables; 1.1 Probability; 1.2 Conditional probability and independence; 1.3 Random variables; 1.4 Random vectors; 1.5 Transformations of random variables; 1.6 Expectation and moments; 1.7 Conditioning; 1.8 Generating functions; 1.9 Multivariate normal; 2 Introduction to stochastic processes; 2.1 Preamble; 2.2 Essential examples; random walks; 2.3 The long run; 2.4 Martingales; 2.5 Poisson processes; 2.6 Renewals; 2.7 Branching processes; 2.8 Miscellaneous models; 2.9 Some technical details; 3 Markov chains; 3.1 The Markov property
  • Examples3.2 Structure and n-step probabilities; 3.3 First-step analysis and hitting times; 3.4 The Markov property revisited; 3.5 Classes and decomposition; 3.6 Stationary distribution: the long run; 3.7 Reversible chains; 3.8 Simulation and Monte Carlo; 3.9 Applications; 4 Markov chains in continuous time; 4.1 Introduction and examples; 4.2 Forward and backward equations; 4.3 Birth processes: explosions and minimality; 4.4 Recurrence and transience; 4.5 Hitting and visiting; 4.6 Stationary distributions and the long run; 4.7 Reversibility; 4.8 Queues; 4.9 Miscellaneous models; 5 Diffusions
  • 5.1 Introduction: Brownian motion5.2 The Wiener process; 5.3 Reflection principle; first-passage times; 5.4 Functions of diffusions; 5.5 Martingale methods; 5.6 Stochastic calculus: introduction; 5.7 The stochastic integral; 5.8 Itô's formula; 5.9 Processes in space; 6 Hints and solutions for starred exercises and problems; Further reading; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W; Y; Z

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