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

## 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.

Item Type: | Article |
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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: | ?? qa ?? |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 2397 |

Deposited By: | ep_importer |

Deposited On: | 01 Apr 2008 09:40 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 23 May 2017 01:32 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/2397 |

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