An almost sure limit theorem for Wick powers of Gaussian differences quotients

Details An almost sure limit theorem for Wick powers of Gaussian differences quotients An almost sure limit theorem for Wick powers of Gaussian differences quotients

2009-10-15

arxiv.org/abs/0910.2932v1

Mathematics

Probability

Scientific paper

Let G={G(x), x\in R_+}, G(0)=0, be a mean zero Gaussian process with $E(G(x)-G(y))^2=\sigma ^2(x-y) $. Let $ \rho (x)= \frac12{d^{2}\over dx^2}\sigma^2(x)$, $x\ne 0 $. When $\rho^{k}$ is integrable at zero and satisfies some additional regularity conditions, \[ \lim_{h\downarrow 0} \int :(\frac{G(x+h)-G(x)}{h})^{k}:g(x) dx=:(G') ^{k}:(g){.3 in}a.s. \] for all $g\in B_{0}(R^{+})$, the set of bounded Lebesgue measurable functions on $R_+$ with compact support. Here $G'$ is a generalized derivative of $G$ and $:(\cd)^{k}:$ is the $k$--th order Wick power.

Affiliated with

Also associated with

No associations

Rating

An almost sure limit theorem for Wick powers of Gaussian differences quotients does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An almost sure limit theorem for Wick powers of Gaussian differences quotients, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An almost sure limit theorem for Wick powers of Gaussian differences quotients will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-620524