Exact Asymptotic for Distribution Densities of Lévy Functionals

Victoria P Knopova (Glushkov Institut of Cybernetics and National Academy of Science of Unkraine)
Alexei M Kulik (National Academy of Sciences of Ukraine)

Abstract


A version of the saddle point method is developed, which allows one to describe exactly the asymptotic behavior of distribution densities of Lévy driven stochastic integrals with deterministic kernels. Exact asymptotic behavior is established for (a) the transition probability density of a real-valued Lévy process; (b) the transition probability density and the invariant distribution density of a Lévy driven Ornstein-Uhlenbeck process; (c) the distribution density of the fractional Lévy motion.

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Pages: 1394-1433

Publication Date: August 10, 2011

DOI: 10.1214/EJP.v16-909

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