On continuous conditional gaussian martingales and stable convergence in law
On decomposability semigroups on the real line
On fully coupled continuous time random walks
Continuous time random walks with jump sizes equal to the corresponding waiting times for jumps are considered. Sufficient conditions for the weak convergence of such processes are established and the limiting processes are identified. Furthermore one-dimensional distributions of the limiting processes are given under an additional assumption.
On measure-preserving transformations and doubly stationary symmetric stable processes
In a 1987 paper, Cambanis, Hardin and Weron defined doubly stationary stable processes as those stable processes which have a spectral representation which is itself stationary, and they gave an example of a stationary symmetric stable process which they claimed was not doubly stationary. Here we show that their process actually had a moving average representation, and hence was doubly stationary. We also characterize doubly stationary processes in terms of measure-preserving regular set isomorphisms...
On Mieshalkin-Rogozin theorem and some properties of the second kind beta distribution
The decomposition of the r.v. X with the beta second kind distribution in the form of finite (formula (9), Theorem 1) and infinity products (formula (17), Theorem 2 and form (21), Theorem 3) are presented. Next applying Mieshalkin - Rogozin theorem we receive the estimation of the difference of two c.d.f. F(x) and G(x) when sup|f(t) - g(t)| is known, improving the result of Gnedenko - Kolmogorov (formulae (23) and (24)).
On some limit distributions for geometric random sums
We define and give the various characterizations of a new subclass of geometrically infinitely divisible random variables. This subclass, called geometrically semistable, is given as the set of all these random variables which are the limits in distribution of geometric, weighted and shifted random sums. Introduced class is the extension of, considered until now, classes of geometrically stable [5] and geometrically strictly semistable random variables [10]. All the results can be straightforward...
On subsets of and -stable processes
On symmetric stable random variables and matrix transposition
On the Bennett–Hoeffding inequality
The well-known Bennett–Hoeffding bound for sums of independent random variables is refined, by taking into account positive-part third moments, and at that significantly improved by using, instead of the class of all increasing exponential functions, a much larger class of generalized moment functions. The resulting bounds have certain optimality properties. The results can be extended in a standard manner to (the maximal functions of) (super)martingales. The proof of the main result relies on an...
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 rate of growth of Lev́y processes with no positive jumps conditioned to stay positive.
On the structure of monoids of admissible translates of probability measures.
On the Unimodality and self-Decomposability of Certain Transformed Distributions
On Urbanik's characterization of Gaussian measures on locally compact abelian groups
Opérateurs réguliers sur les espaces
Operator semistable probability measures on Banach spaces
Operator semistable probability measures on
Operator-stable probability measures on Banach spaces
Optimal transportation for multifractal random measures and applications
In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is intuitively some kind of multistep transportation. Applications are given for construction of multifractal random changes of times and to the existence of random metrics, the volume forms of which coincide with the multifractal random measures.
Partition-dependent stochastic measures and -deformed cumulants.