 A functional law of the iterated logarithm for weakly hypoelliptic diffusions at time zeroMarco Carfagnini, Juraj Földes and David P. Herzog Stochastic Processes and their Applications, 2022, vol. 149, issue C, 188-223 Abstract: We study the almost sure behavior of solutions of stochastic differential equations (SDEs) as time goes to zero. Our main general result establishes a functional law of the iterated logarithm (LIL) that applies in the setting of SDEs with degenerate noise satisfying the weak Hörmander condition but not the strong Hörmander condition. That is, SDEs in which the drift terms must be used in order to conclude hypoellipticity. As a corollary of this result, we obtain the almost sure behavior as time goes to zero of a given direction in the equation, even if noise is not present explicitly in that direction. The techniques used to prove the main results are based on large deviations applied to a non-trivial rescaling of the original system. In concrete examples, we show how to find the proper rescaling to obtain the functional LIL. Furthermore, we apply the main results to the problem of identifying regular points for hypoelliptic diffusions. Consequently, we obtain a control-theoretic criteria for a given point to be regular for the process. Date: 2022 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:149:y:2022:i:c:p:188-223 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2022.03.012 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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