We study the large-time behavior of the charged-polymer Hamiltonian Hn of Kantor and Kardar [Bernoulli case] and Derrida, Griffiths, and Higgs [Gaussian case], using strong approximations to Brownian motion. Our results imply, among other things, that in one dimension the process {H[nt]}0≤t≤1 behaves like a Brownian motion, timechanged by the intersection local-time process of an independent Br...

In this paper, we show how concentration inequalities for Gaussian quadratic form can be used to propose exact confidence intervals of the Hurst index parametrizing a fractional Brownian motion. Both cases where the scaling parameter of the fractional Brownian motion is known or unknown are investigated. These intervals are obtained by observing a single discretized sample path of a fractional ...

In this paper we study harmonic functions of subordinate killed Brownian motion in a domain D: We first prove that, when the killed Brownian semigroup in D is intrinsic ultracontractive, all nonnegative harmonic functions of the subordinate killed Brownian motion in D are continuous and then we establish a Harnack inequality for these harmonic functions. We then show that, when D is a bounded L...

A Hilbert-valued stochastic integration is defined for an integrator that is a cylindrical fractional Brownian motion in a Hilbert space. Since the integrator is not a semimartingale for the fractional Brownian motions considered, a different definition of integration is required. Both deterministic and stochastic operator-valued integrands are used. The approach to integration has an analogue ...

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) which converges back to a Brownian motion with reduced diffusion coefficient at long times, after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membran...

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes...

A fixed 2-dimensional projection of a 3-dimensional Brownian motion is almost surely neighborhood recurrent; is this simultaneously true of all the 2-dimensional projections with probability one? Equivalently: 3-dimensional Brownian motion hits any infinite cylinder with probability one; does it hit all cylinders? This papers shows that the answer is no. Brownian motion in three dimensions avoi...

We give a characterization of G-regularity for super-Brownian motion and the Brownian snake. More precisely, we define a capacity on E = (0,∞)×R, which is not invariant by translation. We then prove that the hitting probability of a Borel set A ⊂ E for the graph of the Brownian snake starting at (0, 0) is comparable, up to multiplicative constants, to its capacity. This implies that super-Brown...

The question of the equivalence in law of Gaussian processes has been widely studied in the sixties-seventies.(5,6,9,14) Recently, the problem has been reopened by several authors, due to the intensive study of the fractional Brownian and of stochastic calculus with respect to this process. Precisely, the Wiener integral representation of the fractional Brownian motion with respect to the Brown...