Mathematics – Probability
Scientific paper
2012-01-27
J. Appl. Probab. Volume 47, Number 4 (2010), 1023-1033
Mathematics
Probability
12 pages, published online at http://projecteuclid.org/euclid.jap/1294170516
Scientific paper
In this paper we study the Wiener-Hopf factorization for a class of L\'evy processes with double-sided jumps, characterized by the fact that the density of the L\'evy measure is given by an infinite series of exponential functions with positive coefficients. We express the Wiener-Hopf factors as infinite products over roots of a certain transcendental equation, and provide a series representation for the distribution of the supremum/infimum process evaluated at an independent exponential time. We also introduce five eight-parameter families of L\'evy processes, defined by the fact that the density of the L\'evy measure is a (fractional) derivative of the theta-function, and we show that these processes can have a wide range of behavior of small jumps. These families of processes are of particular interest for applications, since the characteristic exponent has a simple expression, which allows efficient numerical computation of the Wiener-Hopf factors and distributions of various functionals of the process.
No associations
LandOfFree
Wiener-Hopf factorization for a family of Levy processes related to theta functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Wiener-Hopf factorization for a family of Levy processes related to theta functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Wiener-Hopf factorization for a family of Levy processes related to theta functions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-345480