2018/01/02 by Maria Gordina, Michael Röckner, Gordina, Maria +3
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Mathematical Biology Tumor Growth #Climate Change Policy and Economics
paper · pdf · doi:10.48550/arxiv.1801.00761
We consider a perturbation of a Hilbert space-valued Ornstein--Uhlenbeck\nprocess by a class of singular nonlinear non-autonomous maximal monotone\ntime-dependent drifts. The only further assumption on the drift is that it is\nbounded on balls in the Hilbert space uniformly in time. First we introduce a\nnew notion of generalized solutions for such equations which we call\npseudo-weak solutions and prove that they always exist and obtain pathwise\nestimates in terms of the data of the equation. Then we prove that their laws\nare absolutely continuous with respect to the law of the original\nOrnstein--Uhlenbeck process. In particular, we show that pseudo-weak solutions\nalways have continuous sample paths. In addition, we obtain integrability\nestimates of the associated Girsanov densities. Some of our results concern\nnon-random equations as well, while probabilistic results are new even in\nfinite-dimensional autonomous settings.\n