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Starting from the 1-dimensional complex-valued Ornstein-Uhlenbeck process, we present two natural ways to imply the associated eigenfunctions of the 2-dimensional normal Ornstein-Uhlenbeck operators i...
We consider graded representations of the algebra NC of noncommutative symmetric functions on the Z-linear span of a graded poset P. The matrix coefficients of such a representation give a Hopf morphi...
Let P be a simple lattice polytope. We define an action of the Hecke operators on E(P), the Ehrhart polynomial of P, and describe their effect on the coefficients of E(P). We also describe how the Bri...
Let F be a real quadratic field with ring of integers O and with class number 1. Let Γ be a congruence subgroup of GL2 (O)GL2() . We describe a technique to compute the action of the Hecke operators o...
Stein operators are differential operators which arise within the so-called Stein's method for stochastic approximation. We propose a new mechanism for constructing such operators for arbitrary (conti...
In a recent paper Birke and Bissantz (2008) considered the problem of nonparametric estimation in inverse regression models with convolution-type operators. For multivariate predictors nonparametric m...
The aim of this paper is to examine the notion of random operators from a Fr&het space into a Banach one. Characteristic function, convergence and decomposabitity of random operators are studied.
We prove some results concerning the almost sure approximation 01 contractions in L, by projections, unitary operators or partial isometries. In particular, a unitary operator for which no subseque...
For the absolutely @-summing operators T: X + Y between Banach spaces X and Y we consider martingale inequalities of the type where (dR)F='=c, L: (R, f,P) is a martingale difference sequence and (...
We show that for a von Neumann algebra in standard form with cyclic and separating tracial vector, and some classes of noncommutative processes on it, stopping and integrals of these processes can ...
A condition implying the strong Iaw of large numbers for trajectories of a normal non-contractive operator is given. The condition has been described in terms of a spectral measure, in the spirit o...
We consider a time-inhomogeneous Markov family (X, P,3 corresponding to a symmetric uniformly elliptic divergence form operator. We show that for any rp in the Sobolev space W: n Wi with p = 2 if d...
A Lkvy process on Rd with distribution p at time 1 is denoted by X") = {xi'")]I.T the improper stochastic integral f (s] d ~ : f io)f f with respect to Xtd is definable, its distribulion is denote...

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