Abstract
We prove the Itô–Wentzell formula for processes with values in the space of generalized functions by using the stochastic Fubini theorem and the Itô–Wentzell formula for real-valued processes, appropriate versions of which are also proved.
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The work was partially supported by NSF grant DMS-0653121.
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Krylov, N.V. On the Itô–Wentzell formula for distribution-valued processes and related topics. Probab. Theory Relat. Fields 150, 295–319 (2011). https://doi.org/10.1007/s00440-010-0275-x
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DOI: https://doi.org/10.1007/s00440-010-0275-x