Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155498 | Stochastic Processes and their Applications | 2015 | 48 Pages |
Abstract
We study the simple hypothesis testing problem for the drift coefficient for stochastic fractional heat equation driven by additive noise. We introduce the notion of asymptotically the most powerful test, and find explicit forms of such tests in two asymptotic regimes: large time asymptotics, and increasing number of Fourier modes. The proposed statistics are derived based on Maximum Likelihood Ratio. Additionally, we obtain a series of important technical results of independent interest: we find the cumulant generating function of the log-likelihood ratio; obtain sharp large deviation type results for T→∞T→∞ and N→∞N→∞.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Igor Cialenco, Liaosha Xu,