The Lévy-Khinchin representation of the one class of signed stable measures and some its applications

DOI10.1007/s10440-009-9510-9zbMath1203.28014OpenAlexW1988412231MaRDI QIDQ970516

Nataliya V. Smorodina, M. M. Faddeev

Publication date: 19 May 2010

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-009-9510-9

zbMATH Keywords

limit theoremsPoisson random measuresLévy-Khinchin representationstrictly stable random variable

Mathematics Subject Classification ID

Stochastic integrals (60H05) Random measures (60G57) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (13)

On stable random variables with a complex stability index ⋮ Stable Random Variables with Complex Stability Index, II ⋮ Nonprobabilistic infinitely divisible distributions: the Lévy-Khinchin representation, limit theorems ⋮ On an approximation for the solutions of some evolution equations by the expectations of random walks functionals ⋮ Stable Random Variables with Complex Stability Index, I ⋮ Probabilistic approximation of solutions of the Cauchy problem for some evolution equations ⋮ An Itô calculus for a class of limit processes arising from random walks on the complex plane ⋮ Symmetric \(\alpha\)-stable distributions with noninteger \(\alpha > 2\) and related stochastic processes ⋮ Probabilistic Representation of a Solution of the Cauchy Problem for Evolution Equations with Riemann--Liouville Operators ⋮ Theorems on convergence of stochastic integrals distributions to signed measures and local limit theorems for large deviations ⋮ A probabilistic representation of solution to the Cauchy problem for evolution equation with differential operator of order greater than 2 ⋮ Estimates for functionals of solutions to higher-order heat-type equations with random initial conditions ⋮ Probabilistic representation of solutions for a class of evolution equations

Cites Work

• A distributional approach to multiple stochastic integrals and transformations of the Poisson measure
• Asymptotic Expansion of the Distribution of a Homogeneous Functional of a Strictly Stable Random Vector. II
• Large deviations of sums of independent random variables
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