EE226a - Summary of Lecture 20 Poisson Process
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EE226a - Summary of Lecture 26 Renewal Processes
As the name indicates, a renewal process is one that “renews” itself regularly. That is, there is a sequence of times {Tn, n ∈ Z} such that the process after time Tn is independent of what happened before that time and has a distribution that does not depend on n. We have seen examples of such processes before. As a simple example, one could consider a Poisson process with jump times Tn. As ano...
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A deeper observation is that a Markov chain X starts afresh from its value at some random times called stopping times. Generally, a stopping time is a random time τ that is non-anticipative. That is, we can tell that τ ≤ n from {X0, X1, . . . , Xn}, for any n ≥ 0. A simple example is the first hitting time TA of a set A ⊂ X . Another simple example is TA + 5. A simple counterexample is TA − 1. ...
متن کاملEE 223 : Stochastic Systems : Estimation and Control Spring 2007 Lecture 20 — April 3
20.1.1 Poisson Process Recall the definition of a Poisson Process with rate γ, depicted in Figure 20.1. This is a stochastic process counting the number of arrivals up to time t starting from time 0, (Nt, t ≥ 0), where the interarrival times are exponentially distributed with mean 1/γ. we can refer to this as a Poisson (γ) process The number of points in an interval (a, b] is denoted N(a, b]. P...
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I. SUMMARY Here are the key ideas and results of this important topic. • Section II reviews Kalman Filter. • A system is observable if its state can be determined from its outputs (after some delay). • A system is reachable if there are inputs to drive it to any state. • We explore the evolution of the covariance in a linear system in Section IV. • The error covariance of a Kalman Filter is bou...
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Here are the key ideas and results. • The output of linear time invariant system is the convolution of its impulse response and the input. The system is bounded iff its impulse response is summable. • The transfer function is the Fourier transform of the impulse response. • A system with rational transfer function is causal if the poles are inside the unit circle. It is causally invertible if t...
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تاریخ انتشار 2005