Summary
Consider the solution {X t , 0≦t≦1} of the equation
whereW={W t , 0≦t≦1} is ad-dimensional Wiener process,b is a Lipschitz function from ℝd into ℝd, andX 0 is ad-dimensional functional of the Wiener process.
Under some additional hypotheses onX 0 andb, the Onsager-Machlup functional associated with the anticipating processX is determined with the help of a noncausal version of the Girsanov theorem due to S. Kusuoka.
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The work of D. Naulart was done during a visit to the Laboratoire de Probabilités
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Chaleyat-Maurel, M., Nualart, D. The Onsager-Machlup functional for a class of anticipating processes. Probab. Th. Rel. Fields 94, 247–270 (1992). https://doi.org/10.1007/BF01192445
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DOI: https://doi.org/10.1007/BF01192445
Mathematics Subject Classifications
- 60H07
- 60H10
- 60J65