= Right local time of a continuous semimartingale
{title2=$L_t^{a,+}=|X_t-a|-|X_0-a|-\int_0^t(\mathbf1_{\{X_s>a\}}-\mathbf1_{\{X_s\leq a\}})\,dX_s$}
= Right local time
{synonym}
This normalization uses the left derivative of absolute value in the <Tanaka formula>. Its increasing correction is the right-sided spatial local time; equivalently $(X_t-a)^+=(X_0-a)^++\int_0^t\mathbf1_{\{X_s>a\}}dX_s+\tfrac12L_t^{a,+}$. It need not equal symmetric local time for a general continuous semimartingale with finite-variation mass at the level. In the <smooth convex approximation proof of the Tanaka formula>, the second derivatives are supported on the positive side of the level, agreeing with this convention.
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