Recurrent extensions of self-similar Markov processes and Cramér’s condition II

By V. Rivero. 2005

89 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bf265310a90804ab6a36a3254beacede6102e369

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Citations in the corpus

Tail asymptotics for exponential function-als of L evy processes (2006, unknown): “The main results of the paper are those concerning cases in which Cramér’s condition, and hence the assumptions in [17, 26], are not satisfied.”
Conditioned stable Levy processes and Lamperti representation. (2006, background): “b, and Rivero [12], section 2.”
Continuous time volatility modelling: COGARCH versus Ornstein-Uhlenbeck models (2006, methodology): “It can be derived by a simple transformation applied to Lemma 4 of Rivero [26].”
Lévy integrals and the stationarity of generalised Ornstein-Uhlenbeck processes (2005, methodology): “e.g. de Haan et al. [7], Kl uppelberg et al. [20], Rivero [ 29 ]), we apply results of Goldie [13] and Kesten [17] to deduce heavy tailed behaviour.”
Weak convergence of positive self-similar Markov processes and overshoots of Lévy processes (2004, background): “Let us mention that in these cases, Rivero [12] and [13] studied the different ways to construct an entrance law for the process (Xρ+t, t ≥ 0).”
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]).”
Law of the absorption time of some positive self-similar Markov processes (2009, background): “[28].”
Some explicit identities associated with positive self-similar Markov processes. (2007, methodology): “Another way to prove part (i) of this theorem is to use a result due to Méjane [22] and Rivero [26] which asserts that for a non-arithmetic Lévy process ξ , if Cramer’s condition is satisfied for θ > 0, i.”
Exponential functionals of Levy processes (2005, background): “number r>0 such that P(ξt ∈ rZ) = 1 for all t≥ 0). Then there exists some constant c>0 such that P(I∞ >t) ∼ ct−θ , t→ ∞. This interesting observation has been made by M´ejane [53] and Rivero [58]. It constrasts with the situation when ξis a subordinator (then, obviously, the condition of Co”
On the Lamperti stable processes (2008, background): “ result in [3] give us the sharp estimate in (3.32). (iii) First note that XL is not arithmetic and that under our assumptions the Cramer condition is satised for some >0. Hence from Lemma 4 in [29], we get the sharp estimate (3.33) for the exponential functional I(XL). (iv) Here, we need the fol”