An Extension of the Ocone--Haussmann--Clark Formula for the Compensated Poisson Processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 2, pp. 349-353
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The Sobolev-type spaces $D_{p,1,\alpha }^{CP}$ ($1\le p\le2$) are defined for the compensated Poisson process, and the stochastic integral representation (analogous to the Ocone–Haussmann–Clark formula) is derived for the functionals from these spaces. The formula is given for the computation of the predictable projections of the stochastic derivatives of the above-mentioned functionals.
Keywords:
Ocone–Haussmann–Clark formula, compensated Poisson process, stochastic derivative, predictable projection.
@article{TVP_2008_53_2_a8,
author = {V. Jaoshvili and O. G. Purtukhiya},
title = {An {Extension} of the {Ocone--Haussmann--Clark} {Formula} for the {Compensated} {Poisson} {Processes}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {349--353},
publisher = {mathdoc},
volume = {53},
number = {2},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2008_53_2_a8/}
}
TY - JOUR AU - V. Jaoshvili AU - O. G. Purtukhiya TI - An Extension of the Ocone--Haussmann--Clark Formula for the Compensated Poisson Processes JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2008 SP - 349 EP - 353 VL - 53 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2008_53_2_a8/ LA - ru ID - TVP_2008_53_2_a8 ER -
%0 Journal Article %A V. Jaoshvili %A O. G. Purtukhiya %T An Extension of the Ocone--Haussmann--Clark Formula for the Compensated Poisson Processes %J Teoriâ veroâtnostej i ee primeneniâ %D 2008 %P 349-353 %V 53 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_2008_53_2_a8/ %G ru %F TVP_2008_53_2_a8
V. Jaoshvili; O. G. Purtukhiya. An Extension of the Ocone--Haussmann--Clark Formula for the Compensated Poisson Processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 2, pp. 349-353. http://geodesic.mathdoc.fr/item/TVP_2008_53_2_a8/