Invariance principle for integral type functionals of square-integrable martingales |
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| Institution: | Maria Curie-Skłodowska University, Institute of Mathematics, 20-031 Lublin, Poland |
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| Abstract: | Let Xn = {Xn(t): 0 ⩽ t ⩽1}, n ⩾ 0, be a sequence of square-integrable martingales. The main aim of this paper is to give sufficient conditions under which ∫·0fn (An(t), Xn(t)) dXn(t) converges weakly in D0, 1] to ∫·0f0(A0(t), X0(t)) dX0 (t) as n → ∞, where {An, n ⩾ 0} is some sequence of increasing processes corresponding to the sequence {Xn, n ⩾ 0}. |
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