I've read a proof for existence of solutions to stochastic differential equation from a book of Ikeda and Watanabe and have a question. Is it possible to prove existence (and uniquness) by means of the Banach contraction principle, similarly like in case of ordinary differential equations? It so, could you give a reference?
Thank you for help and hints, Almost sure.
This is actually the usual technique for solving BSDEs(Backward Stochastic Differential Equations). Check out the first (or second) chapter of
Yong, Jiongmin and Zhou, Xun Yu. (1999) Stochastic controls.
and the references to see how this works.