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math.PR2021
An application of the Gaussian correlation inequality to the small deviations for a Kolmogorov diffusion
Marco Carfagnini
We consider an iterated Kolmogorov diffusion of step . The small ball problem for is solved by means of the Gaussian correlation inequality. We also prove Chung'…
math.PR2021
A functional Law of the Iterated Logarithm for weakly hypoelliptic diffusions at time zero
Marco Carfagnini, Juraj Foldes, David P. Herzog
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 iterate…
math.PR2021
On the Support of a hypoelliptic diffusion on the Heisenberg group
Marco Carfagnini
We provide an elementary proof of the support of the law of a hypoelliptic Brownian motion on the Heisenberg group . We consider a control norm associated to left-invar…