随机过程英语讲义-7.pdf

STOCHASTIC PROCESSES AND ITS APPLICATIONS Prof. Xia Yuanqing Assistant Dai Li School of Automation School of Automation Beijing Institute of Technology Beijing Institute of Technology E-mail:yuanqing.xia@ E-mail:daili1887@ 1 Chapter 2 Poisson processes 2.0 Review 2.1 Definition 2.2 Properties of Poisson processes 2.3 Nonhomogeneous Poisson processes 2.4 Compound Poisson processes 2.5 Conditional Poisson processes 2.6 Filtered Poisson processes 2 2.7 Renewal processes 2.0 Review , , 3 2.0 Review , 4 2.0 Review Sum of Poisson Random Variables: 5 2.0 Review 6 2.0 Review Sampling a Poisson Variable: 7 2.0 Review How come? 8 2.1 Definition A stochastic process {N(t) : t ≥0} is a counting process if N(t) represents the total number of “events” that occur by time t. N(t) should satisfy: 1. N(t) ≥0 2. N(t) is integer valued 3. If st, then N(s)≤N (t) 4. For st, N(t)-N(s) equals the number of events that occur in (s, t] 9