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 0178-8051Full text not available from this repository.
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.
|Journal or Publication Title:||Probability Theory and Related Fields|
|Additional Information:||RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics|
|Uncontrolled Keywords:||Azéma martingale - Chaotic-representation property - Normal martingale - Predictable-representation property - Structure equation|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Mathematics and Statistics|
|Deposited On:||01 Apr 2008 09:40|
|Last Modified:||09 Oct 2013 13:12|
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