Backward Itô's formula for sections of a fibered manifold

Hiroshi AKIYAMA

doi:10.2969/jmsj/04220327

Hiroshi AKIYAMA

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JOURNAL FREE ACCESS

1990 Volume 42 Issue 2 Pages 327-340

DOI https://doi.org/10.2969/jmsj/04220327

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Published: 1990 Received: April 05, 1989 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: TITLE Details: Wrong : Backward Ito's formula for sections of a fibered manifold
Right : Backward Itô's formula for sections of a fibered manifold

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H. Akiyama, On Ito's formula for certain fields of geometric objects, J. Math. Soc. Japan, 39 (1987), 79-91.
2) H. Akiyama, Applications of nonstandard analysis to stochastic flows and heat kernels on manifolds, Geometry of Manifolds (ed. by K. Shiohama), Academic Press, Boston, New York, London, 1989, pp. 3-27.
3) R.L. Bishop and R.J. Crittenden, Geometry of Manifolds, Academic Press, New York, London, 1964.
4) M. Ferraris, M. Francaviglia and C. Reina, A constructive approach to bundles of geometric objects on a differentiable manifold, J. Math. Phys., 24 (1983), 120-124.
5) M. Ferraris, M. Francaviglia and C. Reina, Sur les fibrés d'objets géométriques et leurs applications physiques, Ann. Inst. H. Poincaré Phys. Théor., 38 (1983), 371-383.
6) N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, Kodansha/North-Holland, Tokyo/Amsterdam, 1981.
7) N. Ikeda and S. Watanabe, Stochastic flows of diffeomorphisms, Stochastic Analysis and Applications (ed. by M.A. Pinsky), Adv. Probab. Related Topics, 7, Marcel Dekker, New York, 1984, pp. 179-198.
8) S. Kobayashi, Transformation Groups in Differential Geometry, Springer, 1972.
9) S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, I, II, Interscience, New York, 1963, 1969.
10) H. Kunita, Stochastic differential equations and stochastic flows of diffeomorphisms, École d'Été de Probab, de Saint-Flour XII-1982 (ed. by P.L. Hennequin), Lecture Notes in Math., 1097, Springer, 1984, pp. 143-303.
11) S. Salvioli, On the theory of geometric objects, J. Duff. Geom., 7 (1972), 257-278.
12) K. Yano, The Theory of Lie Derivatives and Its Applications, North-Holland, Amsterdam, 1955.

Right : [1] H. Akiyama, On Itô's formula for certain fields of geometric objects, J. Math. Soc. Japan, 39 (1987), 79-91.
[2] H. Akiyama, Applications of nonstandard analysis to stochastic flows and heat kernels on manifolds, Geometry of Manifolds (ed. by K. Shiohama), Academic Press, Boston, New York, London, 1989, pp. 3-27.
[3] R. L. Bishop and R. J. Crittenden, Geometry of Manifolds, Academic Press, New York, London, 1964.
[4] M. Ferraris, M. Francaviglia and C. Reina, A constructive approach to bundles of geometric objects on a differentiable manifold, J. Math. Phys., 24 (1983), 120-124.
[5] M. Ferraris, M. Francaviglia and C. Reina, Sur les fibrés d'objets géométriques et leurs applications physiques, Ann. Inst. H. Poincaré Phys. Théor., 38 (1983), 371-383.
[6] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, Kodansha/North-Holland, Tokyo/Amsterdam, 1981.
[7] N. Ikeda and S. Watanabe, Stochastic flows of diffeomorphisms, Stochastic Analysis and Applications (ed. by M. A. Pinsky), Adv. Probab. Related Topics, 7, Marcel Dekker, New York, 1984, pp. 179-198.
[8] S. Kobayashi, Transformation Groups in Differential Geometry, Springer, 1972.
[9] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, I, II, Interscience, New York, 1963, 1969.
[10] H. Kunita, Stochastic differential equations and stochastic flows of diffeomorphisms, École d'Été de Probab, de Saint-Flour XII-1982 (ed. by P. L. Hennequin), Lecture Notes in Math., 1097, Springer, 1984, pp. 143-303.
[11] S. Salvioli, On the theory of geometric objects, J. Duff. Geom., 7 (1972), 257-278.
[12] K. Yano, The Theory of Lie Derivatives and Its Applications, North-Holland, Amsterdam, 1955.

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