Wiener-Hopf Factorization of Transfer Functions of Extended Pritchard-Salamon Realizations
نویسندگان
چکیده
منابع مشابه
The Wiener-Hopf factorization
We give a description of the classical Wiener-Hopf factorization from the point of view of excursion theory concentrating mainly on the case of random walks as opposed to Lévy processes. The exposition relies primarily on the ideas of Greenwood and Pitman (1979, 1980).
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The key step in the solution of a Wiener–Hopf equation is the decomposition of the Fourier transform of the kernel, which is a function of a complex variable, α say, into a product of two terms. One is singularity and zero free in an upper region of the α-plane, and the other singularity and zero free in an overlapping lower region. Each product factor can be expressed in terms of a Cauchy-type...
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In this paper we study the Wiener–Hopf factorization for a class of Lévy processes with double-sided jumps, characterized by the fact that the density of the Lévymeasure 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 fo...
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ژورنال
عنوان ژورنال: Mathematische Nachrichten
سال: 1998
ISSN: 0025-584X
DOI: 10.1002/mana.19981960105