Euler approximations of anticipating quasilinear stochastic differential equations. (Ukrainian, English) Zbl 1124.60054

Shevchenko, Georgij

Teor. Jmovirn. Mat. Stat. 72, 150-157 (2005); translation in Theory Probab. Math. Stat. 72, 167-175 (2006).

The rate of convergence of the Euler type approximations for the anticipating quasilinear stochastic differential equation \[ X(t)=X_0+\int_{0}^{t}b(s,X(s),\omega)\,ds+\int_0^t\sigma(s)X(s) W(s)\,ds, \] where \(B(t)\) is a Brownian motion, \(W(t)=\dot{B}(t)\) is a white noise process, is estimated.

Reviewer: Mikhail P. Moklyachuk (Kyïv)

MSC:

60H35	Computational methods for stochastic equations (aspects of stochastic analysis)
65C30	Numerical solutions to stochastic differential and integral equations

Keywords:

stochastic differential equation; Euler approximation; Brownian motion