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Note for Signals and Stochastic Process - SSP By Jitendra Pal

  • Signals and Stochastic Process - SSP
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BIJU PATNAIK UNIVERSITY OF TECHNOLOGY, ODISHA Lecture Notes On STOCHASTIC PROCESSES Prepared by, Dr. Subhendu Kumar Rath, BPUT, Odisha.

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Stochastic Processes Dr Subhendu Kumar Rath, Dy. Registrar, BPUT

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Stochastic process X(t) is the state of the process (measurable characteristic of interest) at time t • the state space of the a stochastic process is defined as the set of all possible values that the random variables X(t) can assume • when the set T is countable, the stochastic process is a discrete time process; denote by {Xn, n=0, 1, 2, …} • when T is an interval of the real line, the stochastic process is a continuous time process; denote by {X(t), t≥0}

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Stochastic process Hence, • a stochastic process is a family of random variables that describes the evolution through time of some (physical) process. • usually, the random variables X(t) are dependent and hence the analysis of stochastic processes is very difficult. • Discrete Time Markov Chains (DTMC) is a special type of stochastic process that has a very simple dependence among X(t) and renders nice results in the analysis of {X(t), t∈T} under very mild assumptions.

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