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...
On concentrated probabilities
Let G be a locally compact Polish group with an invariant metric. We provide sufficient and necessary conditions for the existence of a compact set A ⊆ G and a sequence such that for all n. It is noticed that such measures μ form a meager subset of all probabilities on G in the weak measure topology. If for some k the convolution power has nontrivial absolutely continuous component then a similar characterization is obtained for any locally compact, σ-compact, unimodular, Hausdorff topological...
On conditions for SLLN for martingales with identically distributed increments.
On continuous conditional gaussian martingales and stable convergence in law
On convergence and regularity of two-parameter (Δ1) submartingales
On convergence of semimartingales
On convex stochastic processes.
On countable dense random sets
On Covariance Of Spectral Estimates Of Stationary Random Sequence
On cumulative process model and its statistical analysis
The notion of the counting process is recalled and the idea of the ‘cumulative’ process is presented. While the counting process describes the sequence of events, by the cumulative process we understand a stochastic process which cumulates random increments at random moments. It is described by an intensity of the random (counting) process of these moments and by a distribution of increments. We derive the martingale – compensator decomposition of the process and then we study the estimator of the...
On differences of self-adjoint semigroups