H\"ormander-Type Theorem for It\^o Processes and Related Backward SPDEs
classification
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backwardbspdesormander-typeprocessesrelatedtheoremdegeneratedifferential
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A H\"ormander-type theorem is established for It\^o processes and related backward stochastic partial differential equations (BSPDEs). A short self-contained proof is also provided for the $L^2$-theory of linear, possibly degenerate BSPDEs, in which new gradient estimates are obtained.
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