On a class of generalized Takagi functions with linear pathwise quadratic variation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:433

Article

Schied, Alexander

关键词: Generalized Takagi function;    Uniform modulus of continuity;    Pathwise quadratic variation;    Pathwise covariation;    Pathwise Ito calculus;    Follmer integral;   

DOI  :  10.1016/j.jmaa.2015.08.022

来源: Elsevier

【 摘 要 】

We consider a class X of continuous functions on [0, 1] that is of interest from two different perspectives. First, it is closely related to sets of functions that have been studied as generalizations of the Takagi function. Second, each function in X admits a linear pathwise quadratic variation and can thus serve as an integrator in Follmer's pathwise Ito calculus. We derive several uniform properties of the class X. For instance, we compute the overall pointwise maximum, the uniform maximal oscillation, and the exact uniform modulus of continuity for all functions in X. Furthermore, we give an example of a pair x, y E X for which the quadratic variation of the sum x y does not exist. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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