Multiple stochastic integrals appearing in the stochastic Taylor expansions

Satoshi TAKANOBU

doi:10.2969/jmsj/04710067

Satoshi TAKANOBU

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JOURNAL FREE ACCESS

1995 Volume 47 Issue 1 Pages 67-92

DOI https://doi.org/10.2969/jmsj/04710067

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Published: 1995 Received: May 27, 1993 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: CITATION Details: Wrong : B) G. Ben Arous, Flots et series de Taylor stochastiques, Probability Theory and Rel. Fields, 81 (1989), 29-77.
C) F. Castell, Asymptotic expansion of stochastic flows, Probability Theory and Rel. Fields, 96 (1993), 225-239.
F-NC) M. Fliess and D. Normand-Cyrot, Algèbres de Lie nilpotentes, formule de Baker-Campbell-Hausdorff et intégrales itérées de K. T. Chen, Lecture Notes in Math., 920, 1982, pp. 257-267.
H) Y.-Z. Hu, Série de Taylor stochastique et formule de Campbell-Hausdorff, d'après Ben Arous, Lecture Notes in Math., 1526, 1992, pp. 579-586.
J) N. Jacobson, Lie Algebras, Wiley, New York, 1962.
K1) H. Kunita, On the representation of solutions of stochastic differential equations, Lecture Notes in Math., 784, 1980, pp. 282-304.
K2) H. Kunita, On the decomposition of solutions of stochastic differential equations, Lecture Notes in Math., 851, 1981, pp. 213-255.
P) R. S. Palais, A global formulation of the Lie theory of transformation groups, Mem. Amer. Math. Soc., 22 (1957).
S) R. S. Strichartz, The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations, J. Funct. Anal., 72 (1987), 320-345.
T1) S. Takanobu, Diagonal short time asymptotics of heat kernels for certain degenerate second order differential operators of Hörmander type, Publ. Res. Inst. Math. Sci., 24 (1988), 169-203.
T2) S. Takanobu, Diagonal estimates of transition probability densities of certain degenerate diffusion processes, J. Funct. Anal., 91 (1990), 221-236.
Y) Y. Yamato, Stochastic differential equations and nilpotent Lie algebras, Z. Wahr. verw. Geb., 47 (1979), 213-229.

Right : [B] G. Ben Arous, Flots et series de Taylor stochastiques, Probability Theory and Rel. Fields, 81 (1989), 29-77.
[C] F. Castell, Asymptotic expansion of stochastic flows, Probability Theory and Rel. Fields, 96 (1993), 225-239.
[F-NC] M. Fliess and D. Normand-Cyrot, Algèbres de Lie nilpotentes, formule de Baker-Campbell-Hausdorff et intégrales itérées de K. T. Chen, Lecture Notes in Math., 920, 1982, pp. 257-267.
[H] Y. -Z. Hu, Série de Taylor stochastique et formule de Campbell-Hausdorff, d'après Ben Arous, Lecture Notes in Math., 1526, 1992, pp. 579-586.
[J] N. Jacobson, Lie Algebras, Wiley, New York, 1962.
[K1] H. Kunita, On the representation of solutions of stochastic differential equations, Lecture Notes in Math., 784, 1980, pp. 282-304.
[K2] H. Kunita, On the decomposition of solutions of stochastic differential equations, Lecture Notes in Math., 851, 1981, pp. 213-255.
[P] R. S. Palais, A global formulation of the Lie theory of transformation groups, Mem. Amer. Math. Soc., 22 (1957).
[S] R. S. Strichartz, The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations, J. Funct. Anal., 72 (1987), 320-345.
[T1] S. Takanobu, Diagonal short time asymptotics of heat kernels for certain degenerate second order differential operators of Hörmander type, Publ. Res. Inst. Math. Sci., 24 (1988), 169-203.
[T2] S. Takanobu, Diagonal estimates of transition probability densities of certain degenerate diffusion processes, J. Funct. Anal., 91 (1990), 221-236.
[Y] Y. Yamato, Stochastic differential equations and nilpotent Lie algebras, Z. Wahr. verw. Geb., 47 (1979), 213-229.

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