@article{Davis:2018:10.1214/16-AIHP792,
author = {Davis, M and Obój, J and Siorpaes, P},
doi = {10.1214/16-AIHP792},
journal = {Annales de l'Institut Henri Poincaré, Probabilités et Statistiques},
pages = {1--21},
title = {Pathwise stochastic calculus with local times},
url = {http://dx.doi.org/10.1214/16-AIHP792},
volume = {54},
year = {2018}
}

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TY  - JOUR
AB  - We study a notion of local time for a continuous path, defined as a limit ofsuitable discrete quantities along a general sequence of partitions of the timeinterval. Our approach subsumes other existing definitions and agrees with theusual (stochastic) local times a.s. for paths of a continuous semimartingale.We establish pathwise version of the It\^o-Tanaka, change of variables andchange of time formulae. We provide equivalent conditions for existence ofpathwise local time. Finally, we study in detail how the limiting objects, thequadratic variation and the local time, depend on the choice of partitions. Inparticular, we show that an arbitrary given non-decreasing process can beachieved a.s. by the pathwise quadratic variation of a standard Brownian motionfor a suitable sequence of (random) partitions; however, such degeneratebehavior is excluded when the partitions are constructed from stopping times.
AU  - Davis,M
AU  - Obój,J
AU  - Siorpaes,P
DO  - 10.1214/16-AIHP792
EP  - 21
PY  - 2018///
SN  - 0246-0203
SP  - 1
TI  - Pathwise stochastic calculus with local times
T2  - Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
UR  - http://dx.doi.org/10.1214/16-AIHP792
UR  - http://arxiv.org/abs/1508.05984v1
UR  - http://hdl.handle.net/10044/1/42529
VL  - 54
ER  - 

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