Generalized Mehler Semigroups: The Non-Gaussian Case

By Marco Fuhrman, Michael Röckner. 2000

82 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/df23e9d1028e014744cccac69523ab861fbbdec4

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Citations in the corpus

Stochastic Convolutions Driven by Martingales: Maximal Inequalities and Exponential Integrability (2007, background): “0 ∥∥eAt∥∥2 2 H dt < then the procedure from [17] may be easily modified to yield a space E, which is continuously embedded into H−1, where H−1 denotes the completion of the space H endowed with the norm x −1 = A−1x H .”
Martingale-Valued Measures, Ornstein-Uhlenbeck Processes with Jumps and Operator Self-Decomposability in Hilbert Space (2006, methodology): “link between stationarity and logarithmic moments has also been established in [9] using different methods, and by a more indirect route than that given here (see also [ 15 ]).”
Harnack and functional inequalities for generalized Mehler semigroups (2003, background): “where T s denotes the adjoint operator of Ts and l is a negative definite function (or equivalently e l is positive definite) on E with lð0Þ 1⁄4 0: We refer to [8,12,14,20,21] for the background literature and further known results on generalized Mehler semigroups.”
Structural properties of semilinear SPDEs driven by cylindrical stable processes (2008, background): “Note that in [11] it is proved that trajectories of (Xx t ) are càdlàg only in some enlarged Hilbert space U containing H.”
Perturbations of Generalized Mehler Semigroups and Applications to Stochastic Heat Equations with Levy Noise and Singular Drift (2004, methodology): “Then Corollary 6.4 in [ 9 ] gives very general conditions on (Tt )t0 and λ so that Cr,p is tight on ˜”
Stochastic Evolution Equations of Jump Type: Existence, Uniqueness and Large Deviation Principles (2007, methodology): “where W is the H-valued Brownian motion introduced in Section 2, b is a constant vector in H and f is a measurable mapping from X into H. The following Ornstein-Uhlenbeck type stochastic evolution equation was first studied in [CM1] and subsequently by many other authors (cf. e.g. [ FR ]).”
Skew convolution semigroups and affine Markov processes (2005, background): “Skew convolution semigroups and OU-processes on real separable Hilbert spaces were studied in [3, 7, 8, 14, 22, 26].”