Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments

By Serguei Foss, Takis Konstantopoulos, Stan Zachary. 2005

72 citations recorded by the source corpus.

Abstract We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks.

Subfields: Finance, Management Information Systems, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/60c90d687ee2f85c8407f6a7c4ba19cdb0fde170

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Jaap Geluk
2. Jingcheng Liu
3. Qihe Tang
4. Jose H. Blanchet
5. Yiqing Chen
6. Dingcheng Wang
7. Kai Wang Ng
8. Yuebao Wang

In Management Information Systems

1. Jose H. Blanchet
2. Persi Diaconis
3. Sourav Chatterjee

In Management Science and Operations Research

1. Jingcheng Liu
2. Jaap Geluk
3. Qihe Tang
4. Jose H. Blanchet
5. Yiqing Chen
6. Dingcheng Wang
7. Kai Wang Ng
8. Kam Chuen Yuen

Citations in the corpus

• State-dependent importance sampling for regularly varying random walks (2008, background): “Other large deviations results have recently been obtained for heavy-tailed processes with Markovian structure; see, for instance, Foss and Korshunov (2006) and Foss et al. (2007).”
• Asymptotic Tail Probabilities of Sums of Dependent Subexponential Random Variables (2009, background): “Keywords Asymptotic tail probability · Convolution · Dominated variation · Farlie-Gumbel-Morgenstern family · Subexponentiality Mathematics Subject Classification (2000) Primary 62E20 · Secondary 60G70 · 62H20”