Summary
We prove an approximation theorem for stochastic differential equations, under rather weak smoothness conditions on the coefficients, when the driving semimartingales are approximated by continuous semimartingales, in probability, and the solutions are considered in several Banach spaces, defined in terms of different types of the modulus of continuity. Hence Stroock-Varadhan's support theorem is obtained in these spaces, in particular, in appropriate Besov and Hölder spaces.
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Partially supported by the Foundation of National Research n° 2290
Partially supported by the DGICYT grant no PB 90-0452
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Gyöngy, I., Nualart, D. & Sanz-Sole, M. Approximation and support theorems in modulus spaces. Probab. Th. Rel. Fields 101, 495–509 (1995). https://doi.org/10.1007/BF01202782
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DOI: https://doi.org/10.1007/BF01202782