Exact Asymptotic for Distribution Densities of Lévy Functionals

Victoria Knopova · Alexei Kulik

19 citations0/0 files storedElectronic Journal of Probability

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Stochastic processes and financial applications Probability and Statistical Research Probability and Risk Models

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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References

2003Financial Modelling with Jump Processes 2001Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics 2002The Fine Structure of Asset Returns: An Empirical Investigation 2003Stochastic Volatility for Lévy Processes 2006Tempering stable processes 1996On the existence of smooth densities for jump processes 2004On multidimensional Ornstein-Uhlenbeck processes driven by a general Lévy process 2006Fractional Lévy processes with an application to long memory moving average processes

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