Successive approximations of solutions to stochastic functional differential equations (Q1346394)

The author considers the stochastic functional differential equation \[ dx(t)= f(t, x_ t) dt+ g(t, x_ t) dw(t),\quad t\geq 0,\leqno{(*)} \] where \(x(t)= \varphi(t)\), \(t\in I_ 0= [- r,0]\). Applying the successive approximations method the author proves the local existence theorem and next he gives a sufficient condition for the global existence solution of \((*)\).