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Local and global existence for mild solutions of stochastic differential equations. (English) Zbl 0931.60053
Let \[ dX(t)= (AX(t)+ F(t,X(t))) dt= B(t, X(t)) dW(t),\quad X(0)= \xi,\tag{1} \] be a stochastic differential equation of ItĂ´ type in the separable Hilbert space. The author considers the problem of the local and global existence and uniqueness of a mild solution of (1) under more general conditions on the coefficients than Lipschitz and linear growth. The proofs are based on some results for measures of noncompactness and condensing operators.

MSC:
60H20 Stochastic integral equations
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