A First Course in Stochastic Processes

By Samuel Karlin

A First Course in Stochastic Processes focuses on several principal areas of stochastic processes and the diversity of applications of stochastic processes, including Markov chains, Brownian motion, and Poisson processes. The publication first takes a look at the elements of stochastic processes, Markov chains, and the basic limit theorem of Markov chains and applications. Discussions focus on criteria for recurrence, absorption probabilities, discrete renewal equation, classification of states of a Markov chain, and review of basic terminologies and properties of random variables and distribution functions. The text then examines algebraic methods in Markov chains and ratio theorems of transition probabilities and applications. The manuscript elaborates on the sums of independent random variables as a Markov chain, classical examples of continuous time Markov chains, and continuous time Markov chains. Topics include differentiability properties of transition probabilities, birth and death processes with absorbing states, general pure birth processes and Poisson processes, and recurrence properties of sums of independent random variables. The book then ponders on Brownian motion, compounding stochastic processes, and deterministic and stochastic genetic and ecological processes. The publication is a valuable source of information for readers interested in stochastic processes.

• Language: English
• Publisher: Academic Press
• Release date: May 12, 2014
• ISBN: 9781483268095

Samuel Karlin

Samuel Karlin has spent the past twenty years traveling, teaching and playing tennis on six continents in over sixty countries. During that time he lived in South Africa, Thailand and most recently in Japan. Some highlights off the court include climbing Mt. Kilimanjaro, hiking the Inca Trail to Machu Picchu and trekking the Annapurna Circuit in Nepal. A native New Yorker, Samuel received his MA and BA in English from Columbia University and currently lives in Bedford with his son. Love 30 is his first book.

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