For SDE's of the form dX(t)=b(X(t))dt+sigma (X(t))dW(t)where b and
sigma are Lipschitz continuous, it is shown that ifwe consider a
fixed sigma in C^5, bounded and with boundedderivatives, the
random field of solutions is pathwise locallyLipschitz continuous
with respect to b when the space of driftcoefficients is the set
of Lipschitz continuous functions of sublineargrowth endowed with
the sup-norm. Furthermore it is shown that thisresult does not
hold if we interchange the role of b and sigma.However for SDE's
where the coefficient vector fields commutesuitably we show
continuity with respect to the sup-norm on thecoefficients and a
number of their derivatives.

Number of pages | 28 |
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Publication status | Published - 1996 |
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