2014/04/17 by Geiss, Christel, Steinicke, Alexander
#60G51 #60H07 #60H10 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1404.4477
We consider measurable F: Ω× ℝd → ℝ where F(⋅, x) belongs for any x to the Malliavin Sobolev space \mathbbD1,2 (with respect to a Lévy process) and provide sufficient conditions on F and G1,…,Gd ∈ \mathbbD1,2 such that F(⋅, G1,…,Gd) ∈ \mathbbD1,2. The above result is applied to show Malliavin differentiability of solutions to BSDEs (backward stochastic differential equations) driven by Lévy noise where the generator is given by a progressively measurable function f(ω,t,y,z).