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muniangel
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Wiener process and Poisson process

June 29th, 2008, 1:38 am

can Poisson Process transfer to Wiener Process? Conditions? Thank you!
Last edited by muniangel on June 28th, 2008, 10:00 pm, edited 1 time in total.
 
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Alan
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Wiener process and Poisson process

June 29th, 2008, 2:27 pm

No, but you can do this. There is a class of pure-jump Levy processes called alpha-stable processes,where alpha is a parameter in (0,2). As alpha -> 2, you get a Wiener process. The sample path for,say, alpha = 1.9 consists of nothing but jumps but neverthelessl looks a lot like Brownian motion. Unlike a Poisson process, thejump intensity is infinite and the jump sizes are variable. See Cont & Tankov's book for more.Hope it helps,