Geodesic
Localization of the extended stochastic integral
Sbornik. Mathematics, Tome 197 (2006) no. 9, pp. 1273-1295 Cet article a éte moissonné depuis la source Math-Net.Ru

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A sufficient condition for the localization of the extended stochastic integral with respect to a Gaussian measure in an infinite-dimensional space is presented. In the finite-dimensional case, for a vector field $v$ in the Sobolev class a condition ensuring the vanishing divergence of $v$ at the zero set of the field itself is presented. Bibliography: 12 titles. 
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A. M. Gomilko; A. A. Dorogovtsev. Localization of the extended stochastic integral. Sbornik. Mathematics, Tome 197 (2006) no. 9, pp. 1273-1295. http://geodesic.mathdoc.fr/item/SM_2006_197_9_a1/

[1] A. V. Skorokhod, “Ob odnom oboschenii stokhasticheskogo integrala”, Teoriya veroyatn. i ee primen., 20:2 (1975), 223–238 | MR | Zbl

[2] D. Nualart, The Malliavin calculus and related topics, Probability and Its Applications, Springer-Verlag, New York, 1995 | MR | Zbl

[3] D. Nualart, E. Pardoux, “Stochastic calculus with anticipating integrands”, Prob. Theory Related Fields, 78 (1988), 535–581 | DOI | MR | Zbl

[4] A. A. Dorogovtsev, “Rasshirennyi stokhasticheskii integral dlya gladkikh funktsionalov ot belogo shuma”, Ukr. matem. zhurn., 41:11 (1989), 1460–1466 | MR | Zbl

[5] A. A. Dorogovtsev, Stokhasticheskii analiz i sluchainye otobrazheniya v gilbertovom prostranstve, Naukova dumka, Kiev, 1992 | MR | Zbl

[6] B. Saimon, Model $P(\Phi)_2$ evklidovoi kvantovoi teorii polya, Mir, M., 1976 | MR

[7] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki. T. 1. Funktsionalnyi analiz, Mir, M., 1977 | MR | MR | Zbl

[8] Yu. V. Egorov, Lineinye differentsialnye uravneniya glavnogo tipa, Nauka, M., 1984 | MR | Zbl

[9] I. Stein, Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR | MR | Zbl

[10] R. Temam, Uravneniya Nave–Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981 | MR | MR | Zbl

[11] A. S. Calderón, A. Zygmund, “Local properties of solutions of elliptic partial differential equations”, Studia Math., 20 (1961), 171–225 | MR | Zbl

[12] S. Watanabe, Lectures on stochastic differential equations and Malliavin calculus, Springer-Verlag, Berlin, 1984 | MR | Zbl