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In contrast, uncertainty solely about drifts in a continuous time setting of stochastic Itô-processes could be dealt with in a dominated framework of measures which are absolutely continuous with respect to a single reference probability measure.
Moreover, as (epsilon rightarrow 0) one has begin{aligned} {X}^epsilon _{i_1}cdots { X}^epsilon _{i_k} partial _t^s bar{Gamma }_{epsilon, A}rightarrow {X}_{i_1}cdots {X}_{i_k}partial _t^s bar{Gamma }_{A} end{aligned} (5.16 uniformly on compact sets, in a dominated way on all (bar{G}).
Moreover, if (Gamma _A) is the fundamental solution of the operator (L_mathcal {A}) defined in (5.1) one has begin{aligned} {X}^epsilon _{i_1}cdots { X}^epsilon _{i_k} partial _t^s Gamma _{epsilon, A}rightarrow {X}_{i_1}cdots {X}_{i_k}partial _t^s Gamma _{A} end{aligned} (5.10)as (epsilon rightarrow 0) uniformly on compact sets and in a dominated way on subcompacts of (Omega ).
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