A Distributional Approach to Multiple Stochastic Integrals and Transformations of the Poisson Measure

We study a class of ‘nonpoissonian’ transformations of the configuration space and the corresponding transformations of the Poisson measure. For some class of Poisson measures we find conditions which are sufficient for the transformed measure (which in general is nonpoissonian) to be absolutely continuous with respect to the initial Poisson measure and get the expression for the corresponding Radon–Nikodym derivative. To solve this problem we use a distributional approach to Poisson multiple stochastic integrals.     

Conditions for the smoothness of the density of the distribution of the Lp -norm of a Gaussian vector

In this paper sufficient conditions are given for the smoothness indicated in the title. The restrictions on the Gaussian measure are connected only with the dimension of its topological support.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 161–166, 1987.     

Nonstabilized azomethine ylides in the synthesis of aryl cucurbitine derivatives

Nonstabilized azomethine ylides react with 4-arylidene-2-phenyloxazol-5(4H)-ones to form diazaspiro[4.4]nonenes, which were hydrolyzed to aryl cucurbitine derivatives in 35–67% overall yield.     

The Invariant and Quasi-invariant Transformations of the Stable Lévy Processes

Let ξ(t),t∈[0,1] be a strictly stable Lévy process with the index of stability α∈(0,2). By ℘ _ξ we denote the law of ξ in the Skorokhod space . For arbitrary ξ we construct ℘ _ξ -quasi-invariant semigroup of transformations of . Under some nondegeneracy condition on the spectral measure of the stable process we construct ℘ _ξ -quasi-invariant group of transformations of . In symmetric case this group is a group of the invariant transformations.      

On a Family of Complex-Valued Stochastic Processes

Doklady Mathematics - We introduce a family $${{r}_{\lambda }},\lambda \in \mathbb{C}$$ of complex-valued stochastic processes making it possible to construct a probabilistic representation for the...     

Theorems on convergence of stochastic integrals distributions to signed measures and local limit theorems for large deviations

We study properties of symmetric stable measures with index α > 2, α ≠ 2m, m ? \mathbbN m \in \mathbb{N} . Such measures are signed ones, and hence they are not probability measures. For this class of measures, we construct an analogue of the Lévy–Khinchin representation. We show that, in some sense, these signed measures are limit measures for sums of independent random variables. Bibliography: 11 titles.     

Invariant and quasi-invariant transformations of measures that correspond to stable processes with independent increments

Let ξ(t), t ∈ [0, 1], be a strictly stable process with an index of stability α ∈ (0, 2). By we denote the law of ξ in the Skorokhod space [0,1]. For arbitrary strictly stable process ξ, we construct a semigroup of transformations of [0, 1] for which the measure is quasi-invariant. For strictly stable processes with positive and negative jumps, we construct a group of transformations of [0, 1] for which the measure is quasi-invariant. In the symmetric case, this group is a group of invariant transformations. Bibliography: 10 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 339, 2006, pp. 135–149.     

The effect of impurity complexes on the shape of PbTe and Bi2Te3 crystals

The causes of strong dependences of the external shapes of lead and bismuth telluride crystals grown under conditions close to equilibrium on the deviation from stoichiometric composition have been investigated. Auger-analysis of lead telluride and its solid solutions indicates the change in the character of bonding in the subsurface layers connected with appearence of smooth faces not belonging to the equilibrium shapes of pure substances. The surface phase existance has been explained on basis of statistical thermodynamics within the framework of the Guttman model and due to the formation of „the crystalline”︁ impurity complexes in a layer medium in contact with the growing crystal surface. Particles attachment to the crystal under these conditions proceeds in two stages, which facilitates crystal growth.