Hilbert-space of a class of multidimensional stochastic processes
Hitting half-spaces or spheres by Ornstein-Uhlenbeck type diffusions
The purpose of the paper is to provide a general method for computing the hitting distributions of some regular subsets D for Ornstein-Uhlenbeck type operators of the form 1/2Δ + F·∇, with F bounded and orthogonal to the boundary of D. As an important application we obtain integral representations of the Poisson kernel for a half-space and balls for hyperbolic Brownian motion and for the classical Ornstein-Uhlenbeck process. The method developed in this paper is based on stochastic calculus and...
Hitting time of a corner for a reflected diffusion in the square
We discuss the long time behavior of a two-dimensional reflected diffusion in the unit square and investigate more specifically the hitting time of a neighborhood of the origin. We distinguish three different regimes depending on the sign of the correlation coefficient of the diffusion matrix at the point 0. For a positive correlation coefficient, the expectation of the hitting time is uniformly bounded as the neighborhood shrinks. For a negative one, the expectation explodes in a polynomial way...
Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations
This paper is concerned with the Hölder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth...
Hölder norms and the support theorem for diffusions
Hölder versions of Banach space valued random fields.
Holt-Winters method with general seasonality
The paper suggests a generalization of widely used Holt-Winters smoothing and forecasting method for seasonal time series. The general concept of seasonality modeling is introduced both for the additive and multiplicative case. Several special cases are discussed, including a linear interpolation of seasonal indices and a usage of trigonometric functions. Both methods are fully applicable for time series with irregularly observed data (just the special case of missing observations was covered up...
Homogénéisation pour des processus associés à des frontières perméables
Homogeneous chaos revisited
Homogeneous extensions of random measures
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...
Horizontal martingales in vector bundles
How a centred random walk on the affine group goes to infinity
How Paul Lévy saw Jean Ville and martingales.
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.
How to Distinguish Between Record Types
Hsu-Robbins and Spitzer's theorems for the variations of fractional Brownian motion.
Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst.
Hypercontractivity and comparison of moments of iterated maxima and minima of independent random variables.
Hyperdefinite stochastic integration I: The nonstandard theory.