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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.

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