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I got some problems with this homework which I have totally no idea, never got into this field before and I really need some help.

First, we have a wiener process like

enter image description here

Which means the probability of the process drops beneath -3 within the time interval [0,1].

Now the thing is we have to simulate the process by discretize it.

1.Suppose we first discretize the process by 100 points and simulate 10,000 process in this way.

i.e., W(0.01), W(0.02), …., W(1.00).

Note that W(t) – W(t-0.01) ~ N(0,0.01) independently.

2.Using the data obtained at 1., we approximate

enter image description here

by

enter image description here

what is the relationship between this value and the real

enter image description here

(larger, equal to or smaller)?

3.Repeat 1. and 2. by cutting [0,1] into 10,000 points instead. Will the resulting probability increases or decreases?

recon
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  • the only thing i know about is I can simulate wiener process by using BM function in Sim.DiffProc package.. that s all. I am so new that I dnt even know how to simulate a wiener process which has a min limit...guys plz help me orz – recon May 05 '19 at 01:01
  • the answer of all these is at https://stats.stackexchange.com/questions/406590/discretization-simulation-of-a-wiener-process – recon May 05 '19 at 20:10

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