Abstract
LetX be a Brownian motion defined on the line (withX(0)=0) and letY be an independent Brownian motion defined on the nonnegative real numbers. For allt≥0, we define theiterated Brownian motion (IBM),Z, by setting\(Z_t \underline{\underline \vartriangle } X(Y_t )\). In this paper we determine the exact uniform modulus of continuity of the process Z.
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Research supported by NSF grant DMS-9122242.
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Khoshnevisan, D., Lewis, T.M. The uniform modulus of continuity of iterated Brownian motion. J Theor Probab 9, 317–333 (1996). https://doi.org/10.1007/BF02214652
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DOI: https://doi.org/10.1007/BF02214652