Cylindrical Lévy processes in Banach spaces
By David Applebaum, Markus Riedle. 2009
61 citations recorded by the source corpus.
Cylindrical probability measures are finitely additive measures on Banach spaces that have sigma‐additive projections to Euclidean spaces of all dimensions. They are naturally associated to notions of weak (cylindrical) random variable and hence weak (cylindrical) stochastic processes. In this paper we focus on cylindrical Lévy processes. These have (weak) Lévy–Itô decompositions and an associated Lévy–Khintchine formula. If the process is weakly square‐integrable, its covariance operator can be used to construct a reproducing kernel Hilbert space in which the process has a decomposition as an infinite series built from a sequence of uncorrelated bona fide one‐dimensional Lévy processes. This series is used to define cylindrical stochastic integrals from which cylindrical Ornstein–Uhlenbeck processes may be constructed as unique solutions of the associated Cauchy problem. We demonstrate that such processes are cylindrical Markov processes and study their (cylindrical) invariant measures.
Subfields: Applied Mathematics, Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/b1a0381d20edb6750ee04e47db43948188f3fc8d
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In Applied Mathematics
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Citations in the corpus
- Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise (2011, background): “17) ‖E(t)− E(s)‖L (Hδ ,H) C|t− s|δ, t, s 0, δ ∈ [0, 1], from Corollary 4.”