Stochastic Processes, Band 1Wiley, 1983 - 309 Seiten A nonmeasure theoretic introduction to stochastic processes. Considers its diverse range of applications and provides readers with probabilistic intuition and insight in thinking about problems. This revised edition contains additional material on compound Poisson random variables including an identity which can be used to efficiently compute moments; a new chapter on Poisson approximations; and coverage of the mean time spent in transient states as well as examples relating to the Gibb's sampler, the Metropolis algorithm and mean cover time in star graphs. Numerous exercises and problems have been added throughout the text. |
Inhalt
PRELIMINARIES | 1 |
Notes and References | 30 |
ན? | 41 |
Urheberrecht | |
9 weitere Abschnitte werden nicht angezeigt.
Häufige Begriffe und Wortgruppen
assumed birth and death Blackwell's theorem Brownian Bridge Brownian motion process compute conditional distribution Consider continuous-time Markov chain converge convex convex function counting process customers arrive cycle death process define denote the number density distributed with mean distribution F E[time equation equivalently ergodic Example exchangeable random variables exponential with rate exponentially distributed finite given Hence i₁ identically distributed increasing independent and identically inequality interarrival distribution Lemma Let X(t Let X1 limiting probabilities Martingale moment generating function n₁ number of customers obtain occurs P{X₁ P₁ P₂ player Poisson distributed Poisson process process with rate process X(t Proposition prove queue random walk S₁ semi-Markov process sequence server stationary process stochastic process suppose symmetric random walk t₁ T₂ transition probabilities Wald's equation X₁ Y₁ Y₂ yields Z₁ Σ Σ Σ Χ