Stochastic Partial Differential Equations with Lévy Noise: An Evolution Equation ApproachCambridge University Press, 11 paź 2007 - 419 Recent years have seen an explosion of interest in stochastic partial differential equations where the driving noise is discontinuous. In this comprehensive monograph, two leading experts detail the evolution equation approach to their solution. Most of the results appeared here for the first time in book form. The authors start with a detailed analysis of Lévy processes in infinite dimensions and their reproducing kernel Hilbert spaces; cylindrical Lévy processes are constructed in terms of Poisson random measures; stochastic integrals are introduced. Stochastic parabolic and hyperbolic equations on domains of arbitrary dimensions are studied, and applications to statistical and fluid mechanics and to finance are also investigated. Ideal for researchers and graduate students in stochastic processes and partial differential equations, this self-contained text will also interest those working on stochastic modeling in finance, statistical physics and environmental science. |
Inne wydania - Wyświetl wszystko
Stochastic Partial Differential Equations with L Vy Noise: An Evolution ... S. Peszat,Professor J Zabczyk Podgląd niedostępny - 2013 |
Kluczowe wyrazy i wyrażenia
1+ku¹)² A₁ Appendix C Regularization Assume B(Rd Banach space basis of H bounded domain bounded linear operators compact operator Consequently continuous function converges convolution semigroup CZ(Rd D²G defines a Co-semigroup denote densely defined Engel and Nagel finite fractional powers gm K2t heat equation Hence Hilbert space Hilbert-Schmidt operators holds Itô formula Jensen inequality K₂t L₁(H L₁(U La(tm Laplace operator Lemma B.3 Lévy processes Markov processes Markov property Moreover natural number non-negative Note Nuclear and Hilbert-Schmidt number of r-oscillations obtain operator norm orthonormal basis P₁ Pazy proof of Theorem Proposition Q is non-negative-definite refer the reader Regularization of Markov satisfying Section 2.5 self-adjoint semigroup of measures semimartingale sequence sin(în space H sup q(n symmetric Theorem B.20 transition semigroup v(dn w-excessive X(t₁ Yk)u Yosida Zabczyk αξί µ₁ ду