The Entrance Laws of Self-Similar Markov Processes and Exponential Functionals of Lévy Processes

By Jean Bertoin, Marc Yor. 2002

102 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c43819242c464f0df829529ff6f4663b35ffa664

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Citations in the corpus

Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes (2010, methodology): “We will use the following result from [6]: if a non-arithmetic Lévy process X satisfies E[|X1|] < ∞ and E[X1] > 0, then as x → 0+ its corresponding pssMp (Z,Qx) in the Lamperti representation converges weakly (in the sense of finite-dimensional distributions) towards a nondegenerate probability law ”
Bernstein-gamma functions and exponential functionals of Levy Processes (2016, background): “23) and [16] wherein it is shown that E [f (VΨ)] = 1 E[I Ψ ] E [ 1 IΨ f ( 1 IΨ )] for any f ∈ C0 ([0,∞)).”
Law of the absorption time of some positive self-similar Markov processes (2009, background): “In this Section we consider the case when ξ is a spectrally negative Lévy process, i.e. ν(0,∞) ≡ 0 in (1.2) and we exclude the cases when ξ is degenerate, that is when ξ is the negative of a subordinator or a pure drift process.”
Exponential functionals of Levy processes (2005, background): “the limit of the laws Px as x! 0+); see [ 14 ] for details and also Caballero and Chaumont [19] for a recent development.”
Some explicit identities associated with positive self-similar Markov processes. (2007, background): “In [3, 4 ], the authors proved that if a non arithmetic L´evy process satisfies E(| 1|) 0 and every measurable ...”
Recurrent extensions of self-similar Markov processes and Cramér’s condition II (2005, background): “Moreover, the expression of the entrance law associated with n should be compared to the entrance law of Bertoin and Caballero [1] and Bertoin and Yor [3] for positive self-similar Markov processes that drift to oo.”
Weak convergence of positive self-similar Markov processes and overshoots of Lévy processes (2004, background): “The Annals of Probability 2006, Vol. 34, No. 3, 1012–1034 DOI: 10.1214/009117905000000611 © Institute of Mathematical Statistics, 2006”