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The chaotic-representation property for a class of normal martingales

Research output: Contribution to journalJournal article

Published

Journal publication date1/11/2007
JournalProbability Theory and Related Fields
Journal number3-4
Volume139
Number of pages20
Pages543-562
Original languageEnglish

Abstract

Suppose Z=(Zt)t ³ 0Z=(Zt)t0 is a normal martingale which satisfies the structure equation d[Z]t = (a(t)+b(t)Zt-) dZt + dtd[Z]t=((t)+(t)Zt−)dZt+dt
. By adapting and extending techniques due to Parthasarathy and to Kurtz, it is shown that, if α is locally bounded and β has values in the interval [-2,0], the process Z is unique in law, possesses the chaotic-representation property and is strongly Markovian (in an appropriate sense). If also β is bounded away from the endpoints 0 and 2 on every compact subinterval of [0,∞] then Z is shown to have locally bounded trajectories, a variation on a result of Russo and Vallois.

Bibliographic note

RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics