Small Ball Probabilities for the Infinite-Dimensional Ornstein-Uhlenbeck Process in Sobolev Spaces
Probability
2016-03-29 v1
Abstract
While small ball, or lower tail, asymptotic for Gaussian measures generated by solutions of stochastic ordinary differential equations is relatively well understood, a lot less is known in the case of stochastic partial differential equations. The paper presents exact logarithmic asymptotics of the small ball probabilities in a scale of Sobolev spaces when the Gaussian measure is generated by the solution of a diagonalizable stochastic parabolic equation. Compared to the finite-dimensional case, new effects appear in a certain range of the Sobolev exponents.
Keywords
Cite
@article{arxiv.1603.08279,
title = {Small Ball Probabilities for the Infinite-Dimensional Ornstein-Uhlenbeck Process in Sobolev Spaces},
author = {Sergey V. Lototsky},
journal= {arXiv preprint arXiv:1603.08279},
year = {2016}
}