Invariance principle for integral type functionals of square-integrable martingales

Ireneusz Szyszkowski

Stochastic Processes and their Applications, 1987, vol. 24, issue 2, 269-277

Abstract: Let Xn = {Xn(t): 0 [less-than-or-equals, slant] t [less-than-or-equals, slant]1}, n [greater-or-equal, slanted] 0, be a sequence of square-integrable martingales. The main aim of this paper is to give sufficient conditions under which [integral operator]·0fn (An(t), Xn(t)) dXn(t) converges weakly in D[0, 1] to [integral operator]·0f0(A0(t), X0(t)) dX0 (t) as n --> [infinity], where {An, n [greater-or-equal, slanted] 0} is some sequence of increasing processes corresponding to the sequence {Xn, n [greater-or-equal, slanted] 0}.

Keywords: weak; convergence; stochastic; integral; invariance; principle; Doob-Meyer; decomposition (search for similar items in EconPapers)
Date: 1987
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