Poissonian Exponential Functionals, q-Series, q-Integrals, and the Moment Problem for log-Normal Distributions

By Jean Bertoin, Philippe Biane, Marc Yor. 2004

49 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c6a1b841d3dee2b564fd3f4d7f2f32f075c9fbe3

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Citations in the corpus

Tail asymptotics for exponential function-als of L evy processes (2006, background): “The case η = 0 and Bi ≡ 1 has been treated before in [3] and was extended in [20] assuming a certain lower tail condition on Bi.”
Analytic Combinatorics (2009, background): “Biane, Bertoin, and Yor [58] encountered a function identical to (35) in their study of exponential functionals of Poisson processes.”
Stieltjes classes for moment-indeterminate probability distributions (2004, background): “…including the problem of moments, was studied intensively by many researchers; see, for example, the works of Pakes and Khattree (1992), Pakes (1996), (2001), Berg (1995), (1998), Stoyanov (2000), (2002), Gut (2002), Bondesson (2002) and Bertoin et al. (2003), as well as the references therein.”
Bernstein-gamma functions and exponential functionals of Levy Processes (2016, background): “tion about the law of the exponential functionals. Also, the class WB contains some well-known special functions, e.g. the Barnes-gamma function and the qgamma function related to the q-calculus, see [10, 22], [61, Remark 6.4], and the derivation of the analytic properties of WB renders many special”
Exponential functionals of Levy processes (2005, background): “ More precisely, (13) follows immediately from (12), whereas (14) can be derived from the factorization (5) of the exponential law. Finally, (15) is obtained by inversion of the Mellin transform; see [10] for details. • Brownian motion with drift: Take ξt = 2(Bt +bt), where Bis a standard Brownian m”
STOCHASTIC INTEGRALS WITH RESPECT TO L´ EVY PROCESSES AND INFINITELY DIVISIBLE DISTRIBUTIONS (2011, methodology): “A stochastic process {Vt : t ≥ 0} is said to be a generalized Ornstein–Uhlenbeck process if (2.3) Vt = e −Xt ( M + ∫ t 0 eXs−dYs ) with a random variable M independent of {(Xt, Yt)} (Carmona, Petit, and Yor [9, 10]).”