Variation of iterated Brownian motion
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Burdzy, Krzysztof
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American Mathematical Society
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In this paper, we study higher order variations of iterated Brownian motion (IBM) with view towards possible applications to the construction of the stochastic integral with respect to IBM. We prove that the 4-th variation of IBM is a deterministic linear function. This clearly means that the quadratic variation is infinite (although we do not prove this). We show that, in a weak sense, the "signed quadratic variation" of IBM is distributed like Brownian motion.
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Burdzy, K. (1994). Variation of iterated Brownian motion. In Measure-valued processes, stochastic partial differential equations, and interacting systems, D.A. Dawson, ed. CRM Proceedings and Lecture Notes, 5. Providence, R.I.: American Mathematical Society, 35-53.