On the generalized logistic and log-logistic distributions
On the generating functional of a convolution semigroup on a Hilbert-Lie group
On the global maximum of the solution to a stochastic heat equation with compact-support initial data
Consider a stochastic heat equation ∂tu=κ ∂xx2u+σ(u)ẇ for a space–time white noise ẇ and a constant κ>0. Under some suitable conditions on the initial function u0 and σ, we show that the quantities lim sup t→∞t−1sup x∈Rln El(|ut(x)|2) and lim sup t→∞t−1ln E(sup x∈R|ut(x)|2) are equal, as well as bounded away from zero and infinity by explicit multiples of 1/κ. Our proof works by demonstrating quantitatively that the peaks of the stochastic process x↦ut(x) are highly concentrated...
On the group pulse processes. I. Classification
On the group pulse processes. II. Power spectrum of the processes with independent points
On the group pulse processes. III. Power spectrum of the processes with independent intervals
On the Haagerup inequality and groups acting on -buildings
Let be a group endowed with a length function , and let be a linear subspace of . We say that satisfies the Haagerup inequality if there exists constants such that, for any , the convolutor norm of on is dominated by times the norm of . We show that, for , the Haagerup inequality can be expressed in terms of decay of random walks associated with finitely supported symmetric probability measures on . If is a word length function on a finitely generated group , we show that,...
On the hedging of American options in discrete time markets with proportional transaction costs.
On the height of a random set of points in a -dimensional unit cube.
On the helix equation
This paper is devoted to the helices processes, i.e. the solutions H : ℝ × Ω → ℝd, (t, ω) ↦ H(t, ω) of the helix equation where Φ : ℝ × Ω → Ω, (t, ω) ↦ Φ(t, ω) is a dynamical system on a measurable space (Ω, ℱ).More precisely, we investigate dominated solutions and non differentiable solutions of the helix equation. For the last case, the Wiener helix plays a fundamental role. Moreover, some relations with the cocycle equation defined...
On the Heyde theorem for discrete Abelian groups
Let X be a countable discrete Abelian group, Aut(X) the set of automorphisms of X, and I(X) the set of idempotent distributions on X. Assume that α₁, α₂, β₁, β₂ ∈ Aut(X) satisfy . Let ξ₁, ξ₂ be independent random variables with values in X and distributions μ₁, μ₂. We prove that the symmetry of the conditional distribution of L₂ = β₁ξ₁ + β₂ξ₂ given L₁ = α₁ξ₁ + α₂ξ₂ implies that μ₁, μ₂ ∈ I(X) if and only if the group X contains no elements of order two. This theorem can be considered as an analogue...
On the hypercontractivity of Ornstein-Uhlenbeck semigroups with drift
On the hypercontractivity property.
On the increments of the principal value of Brownian local time.
On the Inequality ...pi f(pi) > piif(qi).
On the infinite divisibility of scale mixtures of symmetric α-stable distributions, α ∈ (0,1]
The paper contains a new and elementary proof of the fact that if α ∈ (0,1] then every scale mixture of a symmetric α-stable probability measure is infinitely divisible. This property is known to be a consequence of Kelker's result for the Cauchy distribution and some nontrivial properties of completely monotone functions. It is known that this property does not hold for α = 2. The problem discussed in the paper is still open for α ∈ (1,2).
On the infinite time horizon linear-quadratic regulator problem under a fractional brownian perturbation
In this paper we solve the basic fractional analogue of the classical infinite time horizon linear-quadratic gaussian regulator problem. For a completely observable controlled linear system driven by a fractional brownian motion, we describe explicitely the optimal control policy which minimizes an asymptotic quadratic performance criterion.
On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation
In this paper we solve the basic fractional analogue of the classical infinite time horizon linear-quadratic Gaussian regulator problem. For a completely observable controlled linear system driven by a fractional Brownian motion, we describe explicitely the optimal control policy which minimizes an asymptotic quadratic performance criterion.
On the innovations conjecture of nonlinear filtering with dependent data.
On the integrability of Banach space valued Walsh polynomials