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The chaotic-representation property for a class of normal martingales

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The chaotic-representation property for a class of normal martingales. / Belton, Alexander C. R.; Attal, Stéphane.
In: Probability Theory and Related Fields, Vol. 139, No. 3-4, 01.11.2007, p. 543-562.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Belton, ACR & Attal, S 2007, 'The chaotic-representation property for a class of normal martingales', Probability Theory and Related Fields, vol. 139, no. 3-4, pp. 543-562. https://doi.org/10.1007/s00440-006-0052-z

APA

Belton, A. C. R., & Attal, S. (2007). The chaotic-representation property for a class of normal martingales. Probability Theory and Related Fields, 139(3-4), 543-562. https://doi.org/10.1007/s00440-006-0052-z

Vancouver

Belton ACR, Attal S. The chaotic-representation property for a class of normal martingales. Probability Theory and Related Fields. 2007 Nov 1;139(3-4):543-562. doi: 10.1007/s00440-006-0052-z

Author

Belton, Alexander C. R. ; Attal, Stéphane. / The chaotic-representation property for a class of normal martingales. In: Probability Theory and Related Fields. 2007 ; Vol. 139, No. 3-4. pp. 543-562.

Bibtex

@article{89e668e025b14a5696ee3490b618da7c,
title = "The chaotic-representation property for a class of normal martingales",
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. ",
keywords = "Az{\'e}ma martingale - Chaotic-representation property - Normal martingale - Predictable-representation property - Structure equation",
author = "Belton, {Alexander C. R.} and St{\'e}phane Attal",
note = "RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics",
year = "2007",
month = nov,
day = "1",
doi = "10.1007/s00440-006-0052-z",
language = "English",
volume = "139",
pages = "543--562",
journal = "Probability Theory and Related Fields",
issn = "0178-8051",
publisher = "Springer New York",
number = "3-4",

}

RIS

TY - JOUR

T1 - The chaotic-representation property for a class of normal martingales

AU - Belton, Alexander C. R.

AU - Attal, Stéphane

N1 - RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics

PY - 2007/11/1

Y1 - 2007/11/1

N2 - 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.

AB - 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.

KW - Azéma martingale - Chaotic-representation property - Normal martingale - Predictable-representation property - Structure equation

U2 - 10.1007/s00440-006-0052-z

DO - 10.1007/s00440-006-0052-z

M3 - Journal article

VL - 139

SP - 543

EP - 562

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 3-4

ER -