On a Formula Concerning Stochastic Differentials

Kiyosi Itô

doi:10.1017/S0027763000012216

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In his previous paper [1] the author has stated a formula concering stochastic differentials with the outline of the proof. The aim of this paper is to show this formula in details in a little more general form (Theorem 6).

References

[1] Itô, K.;: On stochastic differential equations in a differentiable manifold, this Journal Vol. 1, 1950.Google Scholar

[2] Itô, K.;: Stochastic differential equations, Memoris of the American Mathematical Society, 4, 1951.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Dynkin, E. B. 1960. Additive Functionals of a Wiener Process Determined by Stochastic Integrals. Theory of Probability & Its Applications, Vol. 5, Issue. 4, p. 402.

Girsanov, I. V. 1960. On Transforming a Certain Class of Stochastic Processes by Absolutely Continuous Substitution of Measures. Theory of Probability & Its Applications, Vol. 5, Issue. 3, p. 285.

Skorokhod, A. V. 1961. Additive Functionals of a Process of Brownian Motion. Theory of Probability & Its Applications, Vol. 6, Issue. 4, p. 396.

Чжань-цюань, Гань 1962. О плотности вероятности перехода для решений стохастических уравнений высших порядков. Ukrainian Mathematical Journal, Vol. 14, Issue. 4, p. 393.

Freidlin, M. I. 1963. Diffusion Processes with Reflection and Problems with a Directional Derivative on a Manifold with a Boundary. Theory of Probability & Its Applications, Vol. 8, Issue. 1, p. 75.

McShane, E. J. 1963. Integrals devised for special purposes. Bulletin of the American Mathematical Society, Vol. 69, Issue. 5, p. 597.

Khas’minskii, R. Z. 1963. Principle of Averaging for Parabolic and Elliptic Differential Equations and for Markov Processes with Small Diffusion. Theory of Probability & Its Applications, Vol. 8, Issue. 1, p. 1.

Tanaka, Hiroshi 1963. Note on continuous additive functional of the 1-dimensional Brownian path. Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 1, Issue. 3, p. 251.

Khas'minskii, R.Z. 1964. The behavior of a conservative system under the action of slight friction and slight random noise. Journal of Applied Mathematics and Mechanics, Vol. 28, Issue. 5, p. 1126.

Gangolli, Ramesh 1964. On the construction of certain diffusions on a differentiable manifold. Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 2, Issue. 5, p. 406.

Wong, Eugene and Zakai, Moshe 1965. The oscillation of stochastic integrals. Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 4, Issue. 2, p. 103.

Eugene, Wong and Moshe, Zakai 1965. On the relation between ordinary and stochastic differential equations. International Journal of Engineering Science, Vol. 3, Issue. 2, p. 213.

Liptser, R. Sh. 1966. A Comparison of Linear and Nonlinear Filtration of Some Markov Processes. Theory of Probability & Its Applications, Vol. 11, Issue. 3, p. 467.

LAX, MELVIN 1966. Classical Noise IV: Langevin Methods. Reviews of Modern Physics, Vol. 38, Issue. 3, p. 541.

Skorokhod, A. V. 1967. Homogeneous Markov Processes without Discontinuities of the Second Kind. Theory of Probability & Its Applications, Vol. 12, Issue. 2, p. 222.

Zakai, Moshe 1967. On the Ultimate Boundedness of Moments Associated with Solutions of Stochastic Differential Equations. SIAM Journal on Control, Vol. 5, Issue. 4, p. 588.

Zakai, Moshe 1967. Some moment inequalities for stochastic integrals and for solutions of stochastic differential equations. Israel Journal of Mathematics, Vol. 5, Issue. 3, p. 170.

Duncan, Tyrone E. 1968. Evaluation of likelihood functions. Information and Control, Vol. 13, Issue. 1, p. 62.

Cabaña, E. M. 1969. On stochastic differentials in Hilbert spaces. Proceedings of the American Mathematical Society, Vol. 20, Issue. 1, p. 259.

Stroock, Daniel W. and Varadhan, S. R. S. 1969. Diffusion processes with continuous coefficients, II. Communications on Pure and Applied Mathematics, Vol. 22, Issue. 4, p. 479.

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