Some time change representations of stable integrals, via predictable transformations of local martingales
From the predictable reduction of a marked point process to Poisson, we derive a similar reduction theorem for purely discontinuous martingales to processes with independent increments. Both results are then used to examine the existence of stochastic integrals with respect to stable Lévy processes, and to prove a variety of time change representations for such integrals. The Knight phenomenon, where possibly dependent but orthogonal processes become independent after individual time changes, emerges as a general principle.
Year of publication: |
1992
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Authors: | Kallenberg, Olav |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 40.1992, 2, p. 199-223
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Publisher: |
Elsevier |
Keywords: | marked point processes purely discontinuous martingales Poisson and sample processes Lévy processes stochastic integrals |
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