You can start with Berman, S.M., Sojourns and Extremes of Stochastic
Processes, The Wadworth and Brooks, Probability Series, 1992. Also, look
for keywords: Crossings of a Level, Rice's Formulae, Rice Series, to begin
with.
- Janusz
On Wed, 2 Aug 2006, Jewel Bright wrote:
> My question, I believe, is a simple one for professionals in
> statistics/random processes.
> Suppose I have a stochastic process described by the Ito SDE. Let's for
> simplicity assume that it is an Ornstein-Ulenbeck Process
> dx(t)=-kx(t)dt+bdW(t)
> I need to study a discrete process associated with the extrema of this
> process.
> In particular, I need to know the distribution of spacings between these
> extrema.
> Note, I am not asking here about any kind of data manipulation or
> estimation work.
> I am asking about theory.
>
> Can anybody advise me any book/papers or other sources which are dealing
> with this kind of problems? Or correct key words/established name of theory
> which studies this subject?
> Thanks
> Jewel
>
>
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