A stability theorem for solutions to backward stochastic differential equations (Q2455168)

The author considers a backward stochastic differential equation of the form \(dY_t=f(Y_t,Z_t)dt + Z_t dW_t\), \(Y_T=\xi\). Under the assumption that there exists a function \(\eta\) such that \(\xi=\eta(W_T)\), the solution \(Y\), \(Z\) of the equation above can be represented as \(Y_t=u(t,W_t)\), \(Z_t=\left. \frac{\partial u(t,x)}{\partial x}\right| _{x=W_t}\), where \(u\) solves a nonlinear parabolic partial differential equation. Based on this representation and a notion of stochastic discrepancy, the author proposes an approximation scheme and states, without proof, a theorem providing an error estimate. It is mentioned that numerical experiments have been performed.