The chaotic-representation property for a class of normal martingales

Belton, Alexander C. R. and Attal, Stéphane (2007) The chaotic-representation property for a class of normal martingales. Probability Theory and Related Fields, 139 (3-4). pp. 543-562. ISSN 0178-8051

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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.

Item Type:
Journal Article
Journal or Publication Title:
Probability Theory and Related Fields
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RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics
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Deposited On:
01 Apr 2008 08:40
Last Modified:
18 Sep 2023 00:11