2019•arXiv (Cornell University)Open access
Large deviations related to the law of the iterated logarithm for Ito\n diffusions
Stefan Gerhold, Christoph Gerstenecker
Open full text 0 citations
Abstract
When a Brownian motion is scaled according to the law of the iterated\nlogarithm, its supremum converges to one as time tends to zero. Upper large\ndeviations of the supremum process can be quantified by writing the problem in\nterms of hitting times and applying a result of Strassen (1967) on hitting time\ndensities. We extend this to a small-time large deviations principle for the\nsupremum of scaled Ito diffusions, using as our main tool a refinement of\nStrassen's result due to Lerche (1986).\n
Open-access reader