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Estimates for the density of functionals of SDEs with irregular drift. (English) Zbl 1279.60070
The authors consider a two-component multidimensional stochastic differential equation whose second component $$Y_t$$ depends on the first component $$X_t$$ which is drifted by a bounded and measurable function $$b(X_t)$$. They obtain a non-trivial integration by parts formula for functions of $$(X_t,Y_t)$$ and, by a Girsanov shift, they derive upper and lower bounds for the density of $$Y_t$$, when $$(X_t,Y_t)$$ is driven by possibly correlated Brownian motions.

##### MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60H07 Stochastic calculus of variations and the Malliavin calculus
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