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Smooth Densities For Degenerate Stochastic Delay Equations With Hereditary Drift, Denis R. Bell, Salah-Eldin A. Mohammed
Smooth Densities For Degenerate Stochastic Delay Equations With Hereditary Drift, Denis R. Bell, Salah-Eldin A. Mohammed
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We establish the existence of smooth densities for solutions of Rd-valued stochastic hereditary differential systems of the form
dx(t) = H(t,x)dt + g(t, x(t - r))dW(t).
In the above equation, W is an n-dimensional Wiener process, r is a positive time delay, H is a nonanticipating functional defined on the space of paths in Rd and g is an n x d matrix-valued function defined on [0, ∞) x Rd, such that gg* has …