Lévy integrals and the stationarity of generalised Ornstein-Uhlenbeck processes

By A. Lindner, Ross Maller. 2005

89 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bc4e5b7d8cf53ca040518507ac1e04acb52fb5f1

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Citations in the corpus

On Exponential Functionals of Lévy Processes (2013, background): “In [27] necessary and sufficient conditions for the existence of causal, strictly stationary solutions of the generalized Ornstein-Uhlenbeck process (2.”
Finite-time ruin probability with an exponential Lévy process investment return and heavy-tailed claims (2009, unknown): “…(1.2) σ 2θ = θ2σ 2, (1.3) νθ (A) = ν({x ∈ R : log(1 + θ(ex − 1)) ∈ A}) for any Borel set A ⊂ R. (1.4) Thus, the IRP Uθ fits into the framework of generalized Ornstein–Uhlenbeck processes, which have recently attracted a lot of attention; see, e.g. Lindner and Maller (2005) or Carmona et al. (2001).”
Fluctuations of Lévy Processes with Applications (2014, background): “For a concise overview of cumulant generating functions, the reader is referred to Lukacs (1970). (4)The continuous time arguments are also given in Kyprianou and Surya (2005) 250 9 Applications to Optimal Stopping Problems”
STOCHASTIC INTEGRALS WITH RESPECT TO L´ EVY PROCESSES AND INFINITELY DIVISIBLE DISTRIBUTIONS (2011, background): “6) is equivalent to the condition E[log |L1|] < ∞, which is also equivalent to E[log |Y1|] < ∞, as [23] says.”
On Continuity Properties of the Law of Integrals of Lévy Processes (2006, unknown): “For a much fuller discussion of conditions for convergence per se we refer to Erickson and Maller [7, 8], who give an overview of known results as well as new results on the ﬁniteness of L´evy integrals.”
Ornstein–Uhlenbeck Processes and Extensions (2009, background): “The stationarity criterion, given in Theorem 2.1 of Lindner and Maller (2005), is that (Xt)t≥0 is strictly stationary, for an appropriate choice of X0, if and only if the integral ∫ ∞ 0 e −ξt−dLt converges (a.s., or, equivalently, in distribution), or else Xt is indistinguishable from a constant…”
Integrated insurance risk models with exponential Lévy investment (2008, background): “4 of Lindner and Maller [16] apply to our situation.”
Method of Moment Estimation in the Cogarch(1,1) Model (2007, unknown): “Then σ2 + falls into the class of generalised Ornstein-Uhlenbeck processes; see [11], Section 5.”
Continuous-time GARCH processes (2006, background): “The Annals of Applied Probability 2006, Vol. 16, No. 2, 790–826 DOI: 10.1214/105051606000000150 © Institute of Mathematical Statistics, 2006”