SLIDE 1
1
2
11.2 Renewal Processes Let X k be i.i.d., with density f , where f is - - PowerPoint PPT Presentation
11.2 Renewal Processes Let X k be i.i.d., with density f , where f is - - PowerPoint PPT Presentation
11.2 Renewal Processes Let X k be i.i.d., with density f , where f is not necessarily exponential. Put and 1 11.2 Renewal Processes Let X k be i.i.d., with density f , where f is not necessarily exponential. Put and The mean function m ( t )
SLIDE 2
SLIDE 3
3
Computing the Renewal Function
The first fact we need is that
SLIDE 4
4
Computing the Renewal Function
The first fact we need is that In general, we won’t know Fk(t).
SLIDE 5
5
Computing the Renewal Function
The first fact we need is that In general, we won’t know Fk(t). In any case, it is now easy to see that since
SLIDE 6
6
Computing the Renewal Function
A more useful formula that you will derive in the problems is the renewal equation
SLIDE 7
7
Computing the Renewal Function
A more useful formula that you will derive in the problems is the renewal equation This integral equation can sometimes be solved in terms of moment generating functions by using Laplace transform methods.
SLIDE 8
8
11.3 The Wiener Process (Brownian Motion)
SLIDE 9
9
11.3 The Wiener Process (Brownian Motion)
trouble follows...
SLIDE 10
10
11.3 The Wiener Process
SLIDE 11
11
SLIDE 12
12
SLIDE 13
13
SLIDE 14
14
SLIDE 15
15
The Wiener Integral
Suppose Xτ is white noise applied to an LTI system
SLIDE 16
16
SLIDE 17
17
SLIDE 18
18
SLIDE 19
19
SLIDE 20
20
The Random Walk Approximation
- f the Wiener Process
SLIDE 21
21
SLIDE 22
22
SLIDE 23
23
SLIDE 24
24