On an identity in law obtained by A. Földes and P. Révész
On an Invariant Borel Measure in Hilbert Space
An example of a nonzero σ-finite Borel measure μ with everywhere dense linear manifold of admissible (in the sense of invariance) translation vectors is constructed in the Hilbert space ℓ₂ such that μ and any shift of μ by a vector are neither equivalent nor orthogonal. This extends a result established in [7].
On an oscillating random walk
On analytic continuation of summability transforms.
On applications of Little's formula.
On asymptotic behaviors and convergence rates related to weak limiting distributions of geometric random sums
Geometric random sums arise in various applied problems like physics, biology, economics, risk processes, stochastic finance, queuing theory, reliability models, regenerative models, etc. Their asymptotic behaviors with convergence rates become a big subject of interest. The main purpose of this paper is to study the asymptotic behaviors of normalized geometric random sums of independent and identically distributed random variables via Gnedenko's Transfer Theorem. Moreover, using the Zolotarev probability...
On asymptotic behaviour of local martingales
On automorphisms of type Arveson systems (probabilistic approach).
On Banach spaces containing . A supplement to the paper by J.Hoffman-Jørgensen “Sums of independent Banach space valued random variables”
On Billard's Theorem for Random Fourier Series
We show that Billard's theorem on a.s. uniform convergence of random Fourier series with independent symmetric coefficients is not true when the coefficients are only assumed to be centered independent. We give some necessary or sufficient conditions to ensure the validity of Billard's theorem in the centered case.
On calculating the Laplace transform of a special quadratic functional of the Ornstein-Uhlenbeck velocity process
On calculation of stationary density of autoregressive processes
An iterative procedure for computation of stationary density of autoregressive processes is proposed. On an example with exponentially distributed white noise it is demonstrated that the procedure converges geometrically fast. The AR(1) and AR(2) models are analyzed in detail.
On certain almost brownian filtrations
On certain probabilities equivalent to coin-tossing, d'après Schachermayer
On certain probabilities equivalent to Wiener measure, d'après Dubins, Feldman, Smorodinsky and Tsirelson
On characterizations of interpolable and minimal stationary processes
On compact Ito's formulas for martingales of mc4.
We prove that the class mc4 of continuous martingales with parameter set [0,1]2, bounded in L4, is included in the class of semi-martingales Sc∞(L0(P)) defined by Allain in [A]. As a consequence we obtain a compact Itô's formula. Finally we relate this result with the compact Itô formula obtained by Sanz in [S] for martingales of mc4.
On complete convergence for -mixingales.
On complete convergence of the sum of a random number of stable type random elements.
On computations with causal compositional models
The knowledge of causal relations provides a possibility to perform predictions and helps to decide about the most reasonable actions aiming at the desired objectives. Although the causal reasoning appears to be natural for the human thinking, most of the traditional statistical methods fail to address this issue. One of the well-known methodologies correctly representing the relations of cause and effect is Pearl's causality approach. The paper brings an alternative, purely algebraic methodology...