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Fermion
Topic Author
Posts: 4486
Joined: November 14th, 2002, 8:50 pm

Ito subtleties

QuoteOriginally posted by: crootP.S.Quote in that limit we expect the t-dependence to disappear, del t becomes insignificant Is this expectation somehow related to "the central limit theorem"?It's a statement that the process becomes progressively more independent of the current state with increasing time (e.g. with decreasing auto-correlation) so that, eventually, the time dependence in del Z disappears (as it should in a and b too). This is the steady-state limit. And since we expect a stable distribution in this limit (since the actual magnitude of a finite del t becomes irrelevant as t->infinity), then a Gaussian is the obvious choice.
Last edited by Fermion on January 16th, 2012, 11:00 pm, edited 1 time in total.

croot
Posts: 104
Joined: July 23rd, 2006, 8:30 pm

Ito subtleties

Quotesince we expect a stable distribution in this limit (since the actual magnitude of a finite del t becomes irrelevant as t->infinity), then a Gaussian is the obvious choice.GBM and CIR disagree.

Fermion
Topic Author
Posts: 4486
Joined: November 14th, 2002, 8:50 pm

Ito subtleties

QuoteOriginally posted by: crootQuotesince we expect a stable distribution in this limit (since the actual magnitude of a finite del t becomes irrelevant as t->infinity), then a Gaussian is the obvious choice.GBM and CIR disagree.We're talking about the density of del Z not x or del x.
Last edited by Fermion on January 16th, 2012, 11:00 pm, edited 1 time in total.

croot
Posts: 104
Joined: July 23rd, 2006, 8:30 pm

Ito subtleties

What if I take Z to be a time-integrated (GBM or CIR) and compute the del Z's from that?
Last edited by croot on January 16th, 2012, 11:00 pm, edited 1 time in total.

Fermion
Topic Author
Posts: 4486
Joined: November 14th, 2002, 8:50 pm

Ito subtleties

QuoteOriginally posted by: crootWhat if I take Z to be a time-integrated (GBM or CIR) and compute the del Z's from that?You can if you like. I am most interested in symmetric distributions and where del z becomes stable in the limit t->infinity.
Last edited by Fermion on January 16th, 2012, 11:00 pm, edited 1 time in total.

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