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A Survey of Stochastic Differential Equations

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Book cover Nonlinear and Convex Analysis in Economic Theory

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 419))

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Abstract

Let us consider a system, dynamical,biological or economical, that is determined by a finite number of parameters:

$$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x}=({{x}^{1}},{{x}^{2}},\ldots,{{x}^{r}})\in{{R}^{r}} $$

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References

Books on stochastic differential equation and related topics

  1. J-M. Bismut, Mécanique aléatoire, Springer Lecture, Notes in Math. 866, Springer, 1981.

    Google Scholar 

  2. K. I. Chung and R. J. Williams, Introduction to stochastic integration, Birkhâuser, 1983.

    Google Scholar 

  3. K. D. Elworthy, Stochastic differential equations on manifolds, Cambridge Univ. Press, 1982.

    Google Scholar 

  4. W. H. Fleming and R. W. Rishel, Deterministic and stochastic optimal control, Springer, 1975.

    Google Scholar 

  5. A. Friedman, Stochastic differential equations and applications, Acad. Press, Vol.1, 1975, and Vol. 2, 1976.

    Google Scholar 

  6. I. Karatzas and S. E. Shreve, Brownian motion and stochastic calculus, Springer, 1988.

    Google Scholar 

  7. N. V. Krylov, Controlled diffusion processes, Springer, 1980.

    Google Scholar 

  8. H. Kunita, Stochastic flows and stochastic differential equations, Cambridge Univ. Press, 1990.

    Google Scholar 

  9. H. Kunita, Stochastic flows and applications, Tata Inst. of Fund. Research, Bombay, 1986.

    Google Scholar 

  10. R. S. Liptser and A. N. Shiryayev, Statistics of random processes I, general theory, 1977 and II,applications, 1978, Springer.

    Google Scholar 

  11. H. P. Mckean, Stochastic integrals, Acad. Press, 1969.

    Google Scholar 

  12. P. Malliavin, Stochastic calculus,Springer, to appear.

    Google Scholar 

  13. M. Nisio, Stochastic control theory, Indian Stat. Institute Lecture Note Series 9, 1980.

    Google Scholar 

  14. L. C. G. Rogers and D. Williams, Diffusions, Markov processes, and martingales, Vol. 2 Itô calculus, J.Waley Si Sons, 1987.

    Google Scholar 

  15. Z. Schuss, Theory and applications of stochastic differential equations, J.Wiley & Sons, 1980.

    Google Scholar 

  16. L. Schwartz, Semimartingales and their stochastic calculus on manifolds, Presses de l’univ. Montréal, 1984.

    Google Scholar 

  17. D. W. Stroock, Lectures on stochastic analysis: diffusion theory, Cambridge Univ. Press, 1987.

    Google Scholar 

  18. D. W. Stroock, Topics in stochastic differential equations, Tata Inst. of Fund. Research, Bombay, 1982.

    Google Scholar 

  19. D. W. Stroock and S. R. S. Varadhan, Multidimensional diffusion processes, Springer, 1979.

    Google Scholar 

  20. S. Watanabe, Stochastic differential equations and Malliavin calculus, Tata Inst. of Fund. Research, Bombay, 1984.

    Google Scholar 

  21. N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes,North-Holland, Kodansha, 1981(1st ed.) and 1989(2nd ed.).

    Google Scholar 

  22. K. Yosida, Functional Analysis, Springer, 1964.

    Google Scholar 

Papers cited in this note

  1. K. Itô, Stochastic differentials, Appl. Math. and Opt. 1 (1974), 374–381.

    Article  Google Scholar 

  2. K. Itô, Stochastic parallel displacement, Springer Lecture Notes in Mathematics 451 (1974), 1–7.

    Article  Google Scholar 

  3. A. Kolmogorov, Ober die analytischen Methoden im der Wakrscheinlichkeitsrechnung, Math. Ann. 104 (1931), 415–458.

    Article  Google Scholar 

  4. W. Feller, Zur Theorie der stochastischen Prozesse (Existenz und Eindentingkaits Sätze), Math. Ann. 113 (1936), 113–160.

    Article  Google Scholar 

  5. R. Fortet, Les fonctions aléatoires du types de Markoff associées à certaines equations linéares aux derivées partielles du type paraboliques, J. Math. Pures Appl. 22 (1943), 177–243.

    Google Scholar 

  6. P. Malliavin, Stochastic calculus of variation and hypo-elliptic operators, Proc. Intern. Symp. SDE Kyoto, 195–263, Kinokuniya, Tokyo, 1978.

    Google Scholar 

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Author information

Authors and Affiliations

  1. RIMS, Kyoto University, Kyoto, 606, Japan

    Kiyosi Itô

Authors
  1. Kiyosi Itô
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Editor information

Editors and Affiliations

  1. Department of Economics Keio University, 2-15-45, Mita, Minato-Ku, Tokyo 108, Japan

    Toru Maruyama (Director of the Conference) (Director of the Conference)

  2. Department of Information Science, Tokyo Institute of Technology, 2-12-1, Ohokayama, Meguro-ku, Tokyo 152, Japan

    Wataru Takahashi (Chief director of the Conference) (Chief director of the Conference)

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© 1995 Springer-Verlag Berlin Heidelberg

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Itô, K. (1995). A Survey of Stochastic Differential Equations. In: Maruyama, T., Takahashi, W. (eds) Nonlinear and Convex Analysis in Economic Theory. Lecture Notes in Economics and Mathematical Systems, vol 419. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48719-4_9

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  • DOI: https://doi.org/10.1007/978-3-642-48719-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58767-5

  • Online ISBN: 978-3-642-48719-4

  • eBook Packages: Springer Book Archive

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