Imperial College London
Alternate

ProfessorRamaCont

Faculty of Natural Sciences, Department of Mathematics

Visiting Professor
 
 
 
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Contact

 

+44 (0)20 7594 0802r.cont Website

 
 
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Location

 

806Weeks BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Cont:2019:btran/34,
author = {Cont, R and Perkowski, N},
doi = {btran/34},
journal = {Transactions of the American Mathematical Society},
pages = {161--186},
title = {Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity},
url = {http://dx.doi.org/10.1090/btran/34},
volume = {6},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We construct a pathwise integration theory, associated with a change of variable formula, for smooth functionals of continuous paths with arbitrary regularity defined in terms of the notion of p-th variation along a sequence of time partitions. For paths with finite p-th variation along a sequence of time partitions, we derive a change of variable formula for p times continuously differentiable functions and show pointwise convergence of appropriately defined compensated Riemann sums. Results for functions are extended to regular path-dependent functionals using the concept of vertical derivative of a functional. We show that the pathwise integral satisfies an `isometry' formula in terms of p-th order variation and obtain a `signal plus noise' decomposition for regular functionals of paths with strictly increasing p-th variation. For less regular (Cp−1) functions we obtain a Tanaka-type change of variable formula using an appropriately defined notion of local time. These results extend to multidimensional paths and yield a natural higher-order extension of the concept of `reduced rough path'. We show that, while our integral coincides with a rough-path integral for a certain rough path, its construction is canonical and does not involve the specification of any rough-path superstructure.
AU  - Cont,R
AU  - Perkowski,N
DO  - btran/34
EP  - 186
PY  - 2019///
SN  - 0002-9947
SP  - 161
TI  - Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity
T2  - Transactions of the American Mathematical Society
UR  - http://dx.doi.org/10.1090/btran/34
UR  - http://arxiv.org/abs/1803.09269v2
UR  - http://hdl.handle.net/10044/1/65012
VL  - 6
ER  -
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