On the favorite points of symmetric L\'evy processes
Bo Li, Yimin Xiao, Xiaochuan Yang
TL;DR
This paper investigates the asymptotic behavior of favorite points in symmetric Lévy processes, extending previous results to a broader class by leveraging Gaussian process tail probability techniques.
Contribution
It extends Marcus's 2001 results on favorite points to more general symmetric Lévy processes using Molchan's approach.
Findings
Characterization of favorite points at zero and infinity
Extension of existing results to broader Lévy process classes
Application of Gaussian tail probability methods
Abstract
This paper is concerned with asymptotic behavior (at zero and at infinity) of the favorite points of L\'evy processes. By exploring Molchan's idea for deriving lower tail probabilities of Gaussian processes with stationary increments, we extend the result of Marcus (2001) on the favorite points to a larger class of symmetric L\'evy processes.
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Taxonomy
TopicsProbability and Risk Models · Stochastic processes and financial applications · Financial Risk and Volatility Modeling