A Large Deviation Principle for Martingales over Brownian Filtration

Mathematics – Probability

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

47 pages

Scientific paper

In this article we establish a large deviation principle for the family {\nu_{\epsilon}:\epsilon \in (0,1)} of distributions of the scaled stochastic processes {P_{-\log\sqrt{\epsilon}}Z_t}_{t\leq 1}, where (Z_t)_{t\in \lbrack 0,1]} is a square-integrable martingale over Brownian filtration and (P_t)_{t\geq 0} is the Ornstein-Uhlenbeck semigroup. The rate function is identified as well in terms of the Wiener-It\^{o} chaos decomposition of the terminal value Z_{1}. The result is established by developing a continuity theorem for large deviations, together with two essential tools, the hypercontractivity of the Ornstein-Uhlenbeck semigroup and Lyons' continuity theorem for solutions of Stratonovich type stochastic differential equations.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

A Large Deviation Principle for Martingales over Brownian Filtration 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 A Large Deviation Principle for Martingales over Brownian Filtration, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Large Deviation Principle for Martingales over Brownian Filtration will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-150657

All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.