Seminar on Stochastics and PDEs: Stefan Geiss

Abstract: We consider mean field backward stochastic differential equations (McKean-Vlasov BSDEs) of the type 
 Y_s^t,x = g (B_T^t,x) + ∫_s ^T f(r,B_r^t,x,Y_r^t,x, Z_r^t,x, [Y_r^0,x₀], [Z_r^0,x₀] ) dr,        t ≤  s ≤T, 
where B_r^t,x := x+B_r-B_t  is a Brownian motion starting at (t,x) ∈ [0,T] x R  and [ξ]   stands for the law of the random variable ξ. 
Under certain conditions on (g,f) we replace this equation by a finite-difference mean field  backward equation driven by a symmetric scaled random walk Bⁿ and provide estimates between the corresponding solutions 
(Y^t,x,Z^t,x) and (Y^n,t,x,Z^n,t,x) in the Wasserstein distance. 
 

This is joint work with B. Djehiche, C. Geiss, C. Labart, and J. Nykänen