extremi of stochastic processes

[Jewel Bright <jwlbright@yahoo.com>]

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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