Ito's formula for non smooth functions like Tanaka's formula

Question

Does there exist an Ito's formula for function of Brownian Motion which are once differentiable but not twice differentiable like Tanaka's formula?

score 4 · Accepted Answer · edited Feb 17 '15 at 17:11

4

Check out Karatzas & Shreve for Ito formulas for difference of convex functions. This normally has local time terms at the non differentiable points but these local time terms disappear in the case given in the question.

edited Feb 17 '15 at 17:11

Johannes Gerer

962

answered Dec 25 '13 at 17:13

Lost1

7,895

score 0 · Answer 2 · answered Jan 13 '17 at 10:58

0

ALso Samuel N. Cohen and Robert J. Elliot show the desired result on page 339 in Stochastic Calculus and Applications (2015).

answered Jan 13 '17 at 10:58

Adsertor Justitia

101

Ito's formula for non smooth functions like Tanaka's formula

2 Answers2