Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] Clark J. M., “The representation of functionals of Brownian motion as stochastic integrals”, Ann. Math. Statist., 41:4 (1970), 1282–1295 | DOI | MR | Zbl

[2] Shiryaev A.N., Ior M., “K voprosu o stokhasticheskikh integralnykh predstavleniyakh funktsionalov ot brounovskogo dvizheniya. I”, Teoriya veroyatn. i ee primen., 48:2 (2003), 375–385 | MR | Zbl

[3] Ma J., Protter P., Martin J. S., “Anticipating integrals for a class of martingales”, Bernoulli, 4 (1998), 81–114 | DOI | MR | Zbl

[4] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976, 543 pp. | MR

[5] Liptser R. Sh., Shiryaev A. N., Teoriya martingalov, Nauka, M., 1986, 512 pp. | MR | Zbl

[6] Purtukhia O., “An extension of the Ocone–Haussmann–Clark formula for a class of normal martingales”, Proceedings of A. Razmadze Mathematical Institute, 132, 2003, 127–136 | MR | Zbl

[7] Jaoshvili V., Purtukhia O., “Stochastic integral representation of functionals of Wiener processes”, Bull. Georg. Acad. Sci., 171:1 (2005), 17–20

[8] Jaoshvili V., Purtukhia O., “Stochastic integral representation of functionals of Poisson processes. I”, Bull. Georg. Acad. Sci., 172:2 (2005), 189–192

[9] Jaoshvili V., Purtukhia O., “Stochastic integral representation of functionals of Poisson processes. II”, Bull. Georg. Acad. Sci., 174:2 (2006), 29–32

[10] Kabanov Yu. M., “Predstavlenie funktsionalov ot vinerovskogo i puassonovskogo protsessov v vide stokhasticheskikh integralov”, Teoriya veroyatn. i ee primen., 28:2 (1973), 376–380