Generalised Ornstein-Uhlenbeck Processes and the Convergence of Levy Integrals

By K. Erickson, Ross Maller. 2005

64 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4a4a6ead2e8b3b0165bfc5e047223deb769f37b4

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Citations in the corpus

Lévy integrals and the stationarity of generalised Ornstein-Uhlenbeck processes (2005, methodology): “We first prove Proposition 2.3 and then Theorem 2.1.”
Additive processes and stochastic integrals (2006, methodology): “In the case of a special type of random integrands, the improper integrals with respect to Lévy processes are studied by Erickson and Maller [3].”
Continuous time volatility modelling: COGARCH versus Ornstein-Uhlenbeck models (2006, background): “Without assuming independence of ξ and η, Erickson and Maller [16], Theorem 2, give necessary and sufficient conditions for the a.s. existence of the integral ∫∞ 0 eξt− dηt.”
On Continuity Properties of the Law of Integrals of Lévy Processes (2006, background): “R Necessary and suﬃcient conditions for the convergence of ∞ 0 e − ξ s − dη s were obtained by Erickson and Maller [7].”
A continuous-time GARCH process driven by a Lévy process: stationarity and second-order behaviour (2004, background): “By a continuous-time analogue of the Goldie–Maller theorem [17], due to Erickson and Maller [15], ∫ ∞ 0 e −Xs ds converges almost surely to a finite random variable if Xt → ∞ almost surely, and σ 2t P−→ ∞ as t → ∞ otherwise.”
Ornstein–Uhlenbeck Processes and Extensions (2009, background): “…necessary and sufficient conditions for the convergence (a.s., or, in distribution) of Lévy integrals of the form ∫ ∞ 0 e−ξt−dLt have been worked out by Erickson and Maller (2005), phrased in terms of quite simple functionals of the canonical triplet of (L, η), which is easily obtained from…”
Tail asymptotics for exponential function-als of L evy processes (2006, unknown): “The result directly follows from Theorem 2 of [15] and the discussion immediately following the statement of the theorem there, keeping in mind the fact that the integrator in our case is deterministic.”
STOCHASTIC INTEGRALS WITH RESPECT TO L´ EVY PROCESSES AND INFINITELY DIVISIBLE DISTRIBUTIONS (2011, background): “6) in terms of the generating triplet of {(Xt, Lt)} is found in Erickson and Maller [14].”