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Unformatted text preview: Introductory Engineering Stochastic Processes, ORIE 361 Instructor: Mark E. Lewis, Associate Professor School of Operations Research and Information Engineering Cornell University Markov Chains – Introduction 1/ 11 Stochastic Processes A stochastic process is a sequence of random variables indexed by time. 2/ 11 Stochastic Processes A stochastic process is a sequence of random variables indexed by time. The value of each random variable usually represents the state of some process. The set of all possible states (for all time is called the state space . 2/ 11 Stochastic Processes A stochastic process is a sequence of random variables indexed by time. The value of each random variable usually represents the state of some process. The set of all possible states (for all time is called the state space . If we follow a realization of a stochastic process for all time, it is called a sample path of the process. 2/ 11 Stochastic Processes A stochastic process is a sequence of random variables indexed by time. The value of each random variable usually represents the state of some process. The set of all possible states (for all time is called the state space . If we follow a realization of a stochastic process for all time, it is called a sample path of the process. Dow Jones Industrial Average (DJIA) graphed over time 2/ 11 Stochastic Processes A stochastic process is a sequence of random variables indexed by time. The value of each random variable usually represents the state of some process. The set of all possible states (for all time is called the state space . If we follow a realization of a stochastic process for all time, it is called a sample path of the process. Dow Jones Industrial Average (DJIA) graphed over time Daily inventory levels 2/ 11 Stochastic Processes A stochastic process is a sequence of random variables indexed by time. The value of each random variable usually represents the state of some process. The set of all possible states (for all time is called the state space . If we follow a realization of a stochastic process for all time, it is called a sample path of the process. Dow Jones Industrial Average (DJIA) graphed over time Daily inventory levels Before viewing the process, the path is unknown. After viewing some portion of the path, ( X 1 , X 2 , . . . , X n ) or { X s , s ≤ t } is called the history up until time n or t , respectively. 2/ 11 Stochastic Processes A stochastic process is a sequence of random variables indexed by time....
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This note was uploaded on 04/03/2008 for the course ORIE 361 taught by Professor Lewis,m. during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 LEWIS,M.

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