Constructing functions with prescribed pathwise quadratic variation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:442

Article

Mishura, Yuliya¹  Schied, Alexander² 

[1] Taras Shevchenko Natl Univ Kyiv, Dept Probabil Stat & Actuarial Math, UA-01601 Kiev, Ukraine

[2] Univ Mannheim, Dept Math, D-68131 Mannheim, Germany

关键词: Pathwise quadratic variation;    Follmer integral;    Pathwise Ito differential equation;    Doss-Sussman method;    Support theorem;    Nowhere differentiability;   

DOI  :  10.1016/j.jmaa.2016.04.056

来源: Elsevier

【 摘 要 】

We construct rich vector spaces of continuous functions with prescribed curved or linear pathwise quadratic variations. We also construct a class of functions whose quadratic variation may depend in a local and nonlinear way on the function value. These functions can then be used as integrators in Follmer's pathwise Ito calculus. Our construction of the latter class of functions relies on an extension of the Doss-Sussman method to a class of nonlinear Ito differential equations for the Follmer integral. As an application, we provide a deterministic variant of the support theorem for diffusions. We also establish that many of the constructed functions are nowhere differentiable. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free