Estimates for the density of functionals of SDEs with irregular drift. (English) Zbl 1279.60070

Kohatsu-Higa, Arturo; Makhlouf, Azmi

Stochastic Processes Appl. 123, No. 5, 1716-1728 (2013).

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.

Reviewer: Nicolas Privault (Singapore)

MSC:

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

Keywords:

stochastic differential equations; density; Malliavin calculus; irregular drift