On mean numbers of passage times in small balls of discretized Itô processes.
On mean value in -quantum spaces
The paper deals with a new mathematical model for quantum mechanics based on the fuzzy set theory [1]. The indefinite integral of observables is defined and some basic properties of the integral are examined.
On mean value theorems for small geodesic spheres in Riemannian manifolds
On mean values of subadditive processes
On Measure Concentration of Vector-Valued Maps
We study concentration properties for vector-valued maps. In particular, we describe inequalities which capture the exact dimensional behavior of Lipschitz maps with values in . To this end, we study in particular a domination principle for projections which might be of independent interest. We further compare our conclusions with earlier results by Pinelis in the Gaussian case, and discuss extensions to the infinite-dimensional setting.
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 Measures of Uniformly Distributed Sequences and Benford's Law.
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 mild solutions of gradient systems in Hilbert spaces
We consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.
On mixing processes and the lost-games distribution
On modelling long term stock returns with ergodic diffusion processes: arbitrage and arbitrage-free specifications.
On modulated random measures.
On moment inequalities and stochastic ordering for weighted reliability measures.
On moments for branching processes
On monotone dependence functions of the quantile type
We introduce the concept of monotone dependence function of bivariate distributions without moment conditions. Our concept gives, among other things, a characterization of independent and positively (negatively) quadrant dependent random variables.
On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes
Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.In this paper the multi-dimensional analog of the Gillis-Weiss random walk model is studied. The convergence of this random walk to a fractional diffusion process governed by a symmetric operator defined as a hypersingular integral or the inverse of the Riesz potential in the sense of distributions is proved.* Supported by German Academic Exchange Service (DAAD).
On multiple-particle continuous-time random walks.
On Multivalued Amarts
In recent years, convergence results for multivalued functions have been developed and used in several areas of applied mathematics: mathematical economics, optimal control, mechanics, etc. The aim of this note is to give a criterion of almost sure convergence for multivalued asymptotic martingales (amarts). For every separable Banach space B the fact that every L¹-bounded B-valued martingale converges a.s. in norm to an integrable B-valued random variable (r.v.) is equivalent to the Radon-Nikodym...
On multivalued martingales, multimeasures and multivalued Radon-Nikodym property
In this paper we prove a representation result for essentially bounded multivalued martingales with nonempty closed convex and bounded values in a real separable Banach space. Then we turn our attention to the interplay between multimeasures and multivalued Riesz representations. Finally, we give the multivalued Radon-Nikodym property.
On nearly selfoptimizing strategies for multiarmed bandit problems with controlled arms
Two kinds of strategies for a multiarmed Markov bandit problem with controlled arms are considered: a strategy with forcing and a strategy with randomization. The choice of arm and control function in both cases is based on the current value of the average cost per unit time functional. Some simulation results are also presented.