Harmonic functions and Hardy spaces on trees with boundaries
Hausdorff dimension of the graph of the fractional Brownian sheet.
Hazard Rates and Subexponential Distributions
Heat kernel asymptotics on the lamplighter group.
Homomorphisms to constructed from random walks
We give a construction of homomorphisms from a group into the reals using random walks on the group. The construction is an alternative to an earlier construction that works in more general situations. Applications include an estimate on the drift of random walks on groups of subexponential growth admitting no nontrivial homomorphism to the integers and inequalities between the asymptotic drift and the asymptotic entropy. Some of the entropy estimates obtained have applications independent of the...
How a centred random walk on the affine group goes to infinity
How the maximum of gaussian random walks and fields is influenced by changes of the variances.
In this paper we present an analytical proof of the fact that the maximum of gaussian random walks exceeds an arbitrary level b with a probability that is an increasing function of the step variances. An analogous result for stochastic integrals is also obtained.