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We discuss the weak convergence of convex stochastic processes. Let {Z n (t):t T}, n 1, be a sequence of stochastic processes, where T is an open convex set of R d , such that Z n :T → R is a convex function (for each ω and each n). We show that {Z n (t):t T 0 } converges weakly to {Z(t):t T}, for each compact set T 0 of T, if and only...
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