Is there a formula like Tanaka's for a censored process?

Question

Say we have a one-dimensionless Ito process, $Z$, but our $f$ isn't smooth, and are trying got figure out the processes of $f(Z)$. I just want to focus on the special case where $Z$ is a $(\mu,\sigma)$ Brownian motion on $(\Omega, \mathcal{F}, P)$. If $f(x)=|x|$, then Tanaka's formula tells us $|Z_t|=\int_{0}^{t} sgn(Z)dZ+\sigma^2l(t,0)$, $t\geq 0$, where $\frac{1}{2\epsilon}\int_0^t 1_{\{|Z(s)|\leq\epsilon\}}ds\rightarrow l(t,0)$, as $t\downarrow 0$.
Is there a similar formula for a $f(x)=max(0,x)=(x)^{+}$?

Answer 1

I found it in a few papers: $$(Z_T)^+=(Z_0)^++\int_0^T 1_{\{Z_s>0\}} dZ_s+\frac{1}{2}l(T,0)$$

Answer 2

The censoring function is the same as the absolute value plus the identity.