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Zbl 0816.60055
Turo, Jan
Successive approximations of solutions to stochastic functional differential equations.
(English)
[J] Period. Math. Hung. 30, No.1, 87-96 (1995). ISSN 0031-5303; ISSN 1588-2829/e

The author considers the stochastic functional differential equation $$dx(t)= f(t, x\sb t) dt+ g(t, x\sb t) dw(t),\quad t\ge 0,\leqno{(*)}$$ where $x(t)= \varphi(t)$, $t\in I\sb 0= [- r,0]$. 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 $(*)$.
[S.Wedrychowicz (Rzeszów)]
MSC 2000:
*60H10 Stochastic ordinary differential equations
34F05 ODE with randomness

Keywords: stochastic functional differential equation; local existence theorem; global existence solution

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