Stein's lemma, Malliavin calculus, and tail bounds, with application to polymer fluctuation exponent

Details Stein's lemma, Malliavin calculus, and tail bounds, with application to polymer fluctuation exponent Stein's lemma, Malliavin calculus, and tail bounds, with application to polymer fluctuation exponent

2009-01-04

arxiv.org/abs/0901.0383v1

Mathematics

Probability

24 pages

Scientific paper

We consider a random variable X satisfying almost-sure conditions involving G:= where DX is X's Malliavin derivative and L^{-1} is the inverse Ornstein-Uhlenbeck operator. A lower- (resp. upper-) bound condition on G is proved to imply a Gaussian-type lower (resp. upper) bound on the tail P[X>z]. Bounds of other natures are also given. A key ingredient is the use of Stein's lemma, including the explicit form of the solution of Stein's equation relative to the function 1_{x>z}, and its relation to G. Another set of comparable results is established, without the use of Stein's lemma, using instead a formula for the density of a random variable based on G, recently devised by the author and Ivan Nourdin. As an application, via a Mehler-type formula for G, we show that the Brownian polymer in a Gaussian environment which is white-noise in time and positively correlated in space has deviations of Gaussian type and a fluctuation exponent \chi=1/2. We also show this exponent remains 1/2 after a non-linear transformation of the polymer's Hamiltonian.

Affiliated with

Also associated with

No associations

Rating

Stein's lemma, Malliavin calculus, and tail bounds, with application to polymer fluctuation exponent 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 Stein's lemma, Malliavin calculus, and tail bounds, with application to polymer fluctuation exponent, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stein's lemma, Malliavin calculus, and tail bounds, with application to polymer fluctuation exponent will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-456536