Tail asymptotics for exponential function-als of L evy processes

By Krishanu Maulik, Bert Zwart. 2006

133 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4ffabf17c4fad9f80faad8eca6b517af4b3768bf

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In Management Science and Operations Research

In Mathematical Physics

Citations in the corpus

Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments (2005, background): “…this result, under appropriate conditions, to an (unmodulated) Lévy process gives a simple proof of the continuous-time version of the Pakes-Veraverbeke Theorem, different from that found in the existing literature—see, e.g., Klüppelberg, Kyprianou and Maller (2004) and Maulik and Zwart (2005).”
Law of the absorption time of some positive self-similar Markov processes (2009, background): “As pointed out by several authors, see Carmona et al. [14], Rivero [40], and, Maulik and Zwart [28], the study of the exponential functional is also motivated by its connection to some interesting random affine equations.”
Bernstein-gamma functions and exponential functionals of Levy Processes (2016, background): “The functions Wφ ∈ WB have already appeared explicitly, see [2, 36, 59, 60] or implicitly, see [18, 47], in the literature.”
Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model (2010, background): “4) Paulsen (2002) obtained relation (3.4) for the special case that {Nt , t ≥ 0} is a Poisson process and {Rt , t ≥ 0} is a Brownian motion with positive drift; see Proposition 4.1 of Paulsen (2002). The reader is also referred to Heyde and Wang (2009) for a result for the finite-time ruin probabili”
Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes (2010, background): “There are results in special cases that correspond to heavy tails, light tails and convolution equivalent tails (see for instance [19, 20, 24, 36, 41, 42]).”
Some simple but challenging Markov processes (2014, background): “See [40, 43, 52, 53, 54, 51, 33] for other works dedicated to this process.”
Exponential functionals of Levy processes (2005, unknown): “Finally, we refer to the recent work [52] for extensions of Corollary 5 to situations where Cramer’s condition is not fulfilled.”
Recurrent extensions of self-similar Markov processes and Cramér’s condition II (2005, background): “This relation is well known; see, for example, [4] and [ 15 ].”
On a Theorem of Breiman and a Class of Random Difference Equations (2007, methodology): “Some partial results can be found in [11] and [19].”