 For a discrete state-space process formula_18, the local time can be expressed more simply as

Tanaka's formula also provides a definition of local time for an arbitrary continuous semimartingale formula_18 on formula_21
A more general form was proven independently by Meyer and Wang; the formula extends Itô's lemma for twice differentiable functions to a more general class of functions.If formula_23 is absolutely continuous with derivative formula_24 which is of bounded variation, then
where formula_26 is the left derivative.If formula_27 is a Brownian motion, then for any formula_28 the field of local times formula_29 has a modification which is a.s. Hölder continuous in formula_30 with exponent formula_31, uniformly for bounded formula_3 and formula_10.