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Exit boundaries of multidimensional SDEs. (English) Zbl 1433.60038
Summary: We show that solutions to multidimensional SDEs with Lipschitz coefficients and driven by Brownian motion never reach the set where all coefficients vanish unless the initial position belongs to that set.
MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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References:
[1] Alexander S. Cherny and Hans-Jürgen Engelbert, Singular stochastic differential equations, Lecture Notes in Mathematics, 1858. Springer-Verlag, Berlin, 2005. · Zbl 1071.60003
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