On the pathwise quadratic variation and local time

Pietro Siorpeas (University of Vienna)
Thursday, October 23, 2014 - 4:00pm
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

Föllmer has shown that one can obtain a pathwise Itô formula for paths which possess quadratic variation along a (fixed) sequence of partitions; this applies of course to a.e. path of any given semimartingale. Here we investigate the extent to which the quadratic variation can depend on the sequence of partitions. Then, we extend Wuermlis work and develop a pathwise Tanaka-Meyer formula for continuous paths which admit pathwise local time, which we prove to exist for a.e. path of a continuous semimartingale. Finally, we describe how the pathwise local time behaves under change of variable and time-change.