Fluctuation Theory for Lévy Processes
@inproceedings{Doney2007FluctuationTF, title={Fluctuation Theory for L{\'e}vy Processes}, author={Ronald A. Doney}, year={2007} }
Recently there has been renewed interest in fluctuation theory for Levy processes. Inthis brief survey we describe several aspects of this topic, including Wiener-Hopf factorisation,the ladder processes, Spitzer’s condition, the asymptotic behaviour of Levy processes at zero and infinity, and other path properties. Some open problems are also presented.
182 Citations
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- Mathematics, Biology
- 2014
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- MathematicsJ. Lond. Math. Soc.
- 2012
This work uses and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual MarkOV process.
Small-Maturity Digital Options in Lévy Models: An Analytic Approach*
- Mathematics
- 2015
We prove a small-time Tauberian theorem for transition probabilities of certain Lévy processes. The main assumption is a condition on the asymptotic behavior of the characteristic function. This…
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- Mathematics
- 2015
Suprema of Lévy processes
- Mathematics
- 2011
In this paper we study the supremum functional Mt=sup0≤s≤tXs, where Xt, t≥0, is a one-dimensional Levy process. Under very mild assumptions we provide a simple, uniform estimate of the cumulative…
Fluctuation theory and stochastic games for spectrally negative Lévy processes
- Mathematics
- 2007
Levy processes have stationary, independent increments. This seemingly unassuming (defining) property leads to a surprisingly rich class of processes which appear in a large number of applications…
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- Mathematics
- 2016
In this paper, we find analytically the upper and lower limits (as the time parameter tends to zero) of the probability that a Lévy process starting at 0 stays positive. We confine ourselves to the…
Exit Problems for Spectrally Negative Processes
- Mathematics
- 2014
This chapter devotees its time to gathering facts about spectrally negative processes, and then to an ensemble of fluctuation identities which are semi-explicit in terms of a class of functions known as scale functions, whose properties the authors shall also explore.
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