## Approximation of BSDE's by Stochastic Difference Equation's

J. Math. Sci. Univ. Tokyo
Vol. 9 (2002), No. 2, Page 257--277.

Nakayama, Toshiyuki
Approximation of BSDE's by Stochastic Difference Equation's
We consider a BSDE (backward stochastic differential equation) % $$\left\{\begin{array}{l} -dY(t)=f(B(\cdot),t,Y(t),Z(t))dt-Z(t)^*dB(t), \ Y(1)=Î¾. \end{array}\right.$$ % We construct backward stochastic difference equations approximating the BSDE, where time and space are discrete. We show the existence and uniqueness of the solutions of the backward stochastic difference equations. Also we show a convergence result of the solutions of the backward stochastic difference equations towards that of the BSDE.