Local time and Tanaka formulae for super Brownian and super stable processes

Robert J. Adler and Marica Lewin

Stochastic Processes and their Applications, 1992, vol. 41, issue 1, 45-67

Abstract: We develop Tanaka-like evolution equations describing the local time Lxt of certain measure valued super processes. For example, if Xt, t [greater-or-equal, slanted] 0, is a planar super Brownian motion and [lambda] > 0 then L = - + [lambda] [integral operator]t0 ds + [integral operator]t0 , where X[Delta] is a martingale measure associated with X, and G[lambda] is the Green's function of a planar Brownian motion (B1t, B2t) standardised to have E[B(i)1]2 = 2. Properties such as the continuity of Lxt in t and x are immediate consequences of these results. En passant, we also establish that Brownian and stable super processes (in the appropriate dimensions) integrate p functions, and derive an Itô formula for these processes more general than others derived previously.

Date: 1992
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