On sums of i.i.d. random variables indexed by N parameters
Some polar sets for the brownian sheet
The gap between the past supremum and the future infimum of a transient Bessel process
The level sets of iterated brownian motion
Fast sets and points for fractional brownian motion
On the global maximum of the solution to a stochastic heat equation with compact-support initial data
Consider a stochastic heat equation = 2+() for a space–time white noise and a constant >0. Under some suitable conditions on the initial function 0 and , we show that the quantities lim sup →∞−1sup ∈ln E(| ()|2) and lim sup →∞−1ln E(sup ∈| ()|2) are equal, as well as bounded away from zero and infinity by explicit multiples of 1/. Our proof works by demonstrating quantitatively that the peaks of...
Stochastic calculus and the continuity of local times of Lévy processes
Intersection Local Times and Tanaka Formulas
On the explosion of the local times along lines of brownian sheet
Chung's law of the iterated logarithm for iterated brownian motion
Lévy classes and self-normalization.
Initial measures for the stochastic heat equation
We consider a family of nonlinear stochastic heat equations of the form , where denotes space–time white noise, the generator of a symmetric Lévy process on , and is Lipschitz continuous and zero at 0. We show that this stochastic PDE has a random-field solution for every finite initial measure . Tight a priori bounds on the moments of the solution are also obtained. In the particular case that for some , we prove that if is a finite measure of compact support, then the solution is...
Intermittence and nonlinear parabolic stochastic partial differential equations.
A note on a.s. finiteness of perpetual integral functionals of diffusions.
Sectorial local non-determinism and the geometry of the Brownian sheet.
Capacity estimates, boundary crossings and the Ornstein-Uhlenbeck process in Wiener space.
Limsup random fractals.
An extreme-value analysis of the LIL for Brownian motion.
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