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A note on strong, non-anticipating solutions for stochastic differential equations: When is path-wise uniqueness necessary?

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Part of the Lecture Notes in Mathematics book series (LNM,volume 939)

Abstract

A necessary and sufficient condition for obtaining strong, non-anticipating solutions is given. As a corollary, we show that path-wise uniqueness is necessary for the existence of strong solutions in a large class of stochastic differential equations.

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References

  1. J. Fujisaki, G. Kallianpur, H. Kunita, Stochastic differential equations for the nonlinear filtering problem, Osaka J. Math. 1 (1972), 19–40.

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  2. R. S. Liptser and A. N. Shiryayev, Statistics of Random Processes, Springer-Verlag, New York, 1977.

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  3. T. Yamada and S. Watanabe, On the uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ. 11 (1971), 155–167.

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© 1982 Springer-Verlag

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Allinger, D. (1982). A note on strong, non-anticipating solutions for stochastic differential equations: When is path-wise uniqueness necessary?. In: Chao, JA., Woyczyński, W.A. (eds) Martingale Theory in Harmonic Analysis and Banach Spaces. Lecture Notes in Mathematics, vol 939. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096253

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  • DOI: https://doi.org/10.1007/BFb0096253

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11569-4

  • Online ISBN: 978-3-540-39284-2

  • eBook Packages: Springer Book Archive