We present detailed discussions on the stochastic Hamiltonians for non-critical string field theories on the basis of matrix models. Beginning from the simplest c=0 case, we derive the explicit forms of the Hamiltonians for the higher critical case k=3 (which corresponds to c=-22/5) and for the case c=1/2, directly from the double-scaled matrix models. In particular, for the two-matrix case, we do not put any restrictions on the spin configurations of the string fields. The properties of the

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... ulting infinite algebras of Schwinger-Dyson operators associated with the Hamiltonians and the derivation of the Virasoro and W_3 algebras therefrom are also investigated. Our results suggest certain universal structure of the stochastic Hamiltonians, which might be useful for an attempt towards a background independent string field theory.