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Non-degeneracy of Wiener functionals arising from rough differential equations. (English) Zbl 1175.60034
The authors consider the stochastic differential equation of type: \[ dY=V(Y)dX+V_0(Y)dt,\tag{1} \] where \(X\) is a non-degenerate multidimensional Gaussian proces. The signal \(X\) is such, that the equation (1) makes sense as rough differential equation. The authors prove the existence of a density for solutions to equation (1). In demonstration of this result they combine some facts of theory of Malliavin calculus and rough paths analysis.

MSC:
60G15 Gaussian processes
60H07 Stochastic calculus of variations and the Malliavin calculus
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60K99 Special processes
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