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
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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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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