Small deviations and Chung's law of iterated logarithm for a hypoelliptic Brownian motion on the Heisenberg group
Marco Carfagnini, Maria Gordina
TL;DR
This paper investigates the small deviations and Chung's law of iterated logarithm for hypoelliptic Brownian motion on the Heisenberg group, providing new bounds and insights into its probabilistic behavior.
Contribution
It introduces new results on small deviations and Chung's law for hypoelliptic Brownian motion in the Heisenberg group, including bounds on the limit behavior.
Findings
Proved small ball probability estimates for the process.
Established Chung's law of iterated logarithm in this setting.
Derived bounds on the limit in Chung's law.
Abstract
A small ball problem and Chung's law of iterated logarithm for a hypoelliptic Brownian motion in Heisenberg group are proven. In addition, bounds on the limit in Chung's law are established.
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Taxonomy
TopicsStochastic processes and financial applications · advanced mathematical theories · Stochastic processes and statistical mechanics