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abstract:
Existence and uniqueness of (analytically weak) linear rough partial differential equations with possibly degenerate second order linear differential operator in the drift term and first order linear differential operators in the dispersion term are proven, both forward and backward in time.
Plugging in the path lift of Brownian motion, we obtain in particular robust pathwise solutions of the corresponding linear stochastic partial differential equations. As an application Wong-Zakai approximation results to linear stochastic partial differential equations are obtained.
The talk is based on joint work with J. Diehl and P. Friz. |
