Invariance of Stochastic integral with respect to the choice of partitions
Abstract
We study the concept of quadratic variation of a continuous path along a sequence of partitions and its dependence with respect to the choice of the partition sequence. We introduce the concept of quadratic roughness of a path along a partition sequence and show that for Hölder-continuous paths satisfying this roughness condition, the quadratic variation along balanced partitions is invariant with respect to the choice of the partition sequence. We further present several constructions of paths and processes with finite quadratic variation along a refining sequence of partitions and, in particular, study the dependence of quadratic variation with respect to the sequence of partitions for these constructions.
About the speaker
Purba Das is a Lecturer (Assistant Professor) in Financial Mathematics in the Department of Mathematics at King's College London. Before KCL, she was a Byrne Research Assistant Professor of Mathematics at the University of Michigan for one year. She completed her DPhil in Mathematics at the University of Oxford under the supervision of Professor Rama Cont.