Variation of local time and new extensions to Ito's formula
Chunrong Feng
2134/35849
https://repository.lboro.ac.uk/articles/thesis/Variation_of_local_time_and_new_extensions_to_Ito_s_formula/9374315
In this doctoral thesis, first we prove the continuous semimartingale local time Lt is of
bounded p-variation in the space variable in the classical sense for any p > 2 a.s., and
based on this fact we define the integral of local time in the sense of Young integral, and
in the sense of Lyons' rough path integral, so that we obtain the new extensions to Tanaka–Meyer's
formula for more classes of f. We also give new conditions to two-parameter Young
integral and extend Elworthy–Truman–Zhao's formula. In the final part we define a new
integral, i.e. stochastic Lebesgue–Stieltjes integral and extend Tanaka–Meyer's formula to
two dimensions.
2018-11-08 15:54:03
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Mathematical Sciences not elsewhere classified