Transcription of Stochastic Process and Markov Chains
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Stochastic Process and Markov Chains
1 Stochastic Process and Markov Stochastic Process and Markov ChainsChainsDavid TipperAssociate ProfessorAssociate ProfessorGraduate Telecommunications and Networking ProgramUniversity of processes A Stochastic Process is a mathematical model for describing an empirical Process that changes in time according to some probabilistic A Stochastic Process is a family of random variables {X(t), t T} defined on a given probability space S, indexed by the parameter t,where t is in an index set T. For each t T, X(t) is a random variable with F(x,t) = P{X(t) x} A realization of X(t) is called a sample pathTelcom 21302 A realization of X(t) is called a sample path Characterization of a Stochastic Space S, set of Stochastic processes State Space The values assumed by a random variable X(t)are called states and the collection of all possible values pforms the state space S of the Process .
Stochastic Process and Markov Chains ... Stochastic Processes ... The probability of making a transition from a state back to itself are and ...
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