TY - JOUR
A2 - Srivastava, H.
AU - Balan, Raluca M.
PY - 2014
DA - 2014/02/04
TI - SPDEs with -Stable Lévy Noise: A Random Field Approach
SP - 793275
VL - 2014
AB - This paper is dedicated to the study of a nonlinear SPDE on a bounded domain in Rd, with zero initial conditions and Dirichlet boundary, driven by an α-stable Lévy noise Z with α∈(0,2), α≠1, and possibly nonsymmetric tails. To give a meaning to the concept of solution, we develop a theory of stochastic integration with respect to this noise. The idea is to first solve the equation with “truncated” noise (obtained by removing from Z the jumps which exceed a fixed value K), yielding a solution uK, and then show that the solutions uL,L>K coincide on the event t≤τK, for some stopping times τK converging to infinity. A similar idea was used in the setting of Hilbert-space valued processes. A major step is to show that the stochastic integral with respect to ZK satisfies a pth moment inequality. This inequality plays the same role as the Burkholder-Davis-Gundy inequality in the theory of integration with respect to continuous martingales.
SN - 2090-3332
UR - https://doi.org/10.1155/2014/793275
DO - 10.1155/2014/793275
JF - International Journal of Stochastic Analysis
PB - Hindawi Publishing Corporation
KW -
ER -