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For the stochastic viability problem of the form
dx(t) ∈ F(t,x(t))dt+g(t,x(t))dW(t), x(t) ∈ K(t),
where K, F are set-valued maps which may have nonconvex values, g is a single-valued function, we establish the existence of solutions under the assumption that F and g possess Lipschitz property and satisfy some tangential conditions.
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