An Introduction to Stochastic Processes and Their Applications
Random variables. Probability generating functions. Exponential-type distributions and maximum likelihood estimation. Branching process, random walk and ruin problem. Markov chains. Algebraic treatment of finite Markov chains. Renewal processes. Some stochastic models of population growth. A general birth process, an equality and an epidemic model. Birth-death processes and queueing processes. A simple illness-death process - fix-neyman processes. Multiple transition probabilities in the simple illness death process. Multiple transition time in the simple illness death process - an alternating renewal process. The kolmogorov differential equations and finite markov processes. Kolmogorov differential equations and finite markov processes - continuation. A general illness-death process. Migration processes and birth-illness-death processes.
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PROBABILITY GENERATING FUNCTIONS
EXPONENTIALTYPE DISTRIBUTIONS AND MAXIMUM
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According apply assume becomes binomial birth called Chapter column complex components compute conditional Consider constant Continuation convolution corresponding death defined denoted density function dependent Derive determinant differential equations discussed distinct distribution function eigenvalues equal estimator event example exists expectation explicit exponential finite formula genotype given hand hence holds identity independent individual initial integral intensity interval introduce lemma length limiting Markov chain matrix mean multiple obtain occur parameter passage Poisson population present probability distribution problem Proof prove queue random variables relation renewal renewal process respectively result roots sample satisfy sequence Show side simple solution Solve stochastic Substituting success Theorem transition probabilities trials values variance vector verify write yields zero