Abstract
In our previous paper [5], we have obtained a decomposition of ∣f∣, where f is a function defined on Rd, that is analogous to the one proved by H. Tanaka in the early sixties for Brownian martingales (the so-called ‘Tanaka formula’). The original proofs use purely analytic methods (e.g. the Calderon–Zygmund theory, etc.). In this paper, we give a new proof of our `Tanaka formula in analysis’, that is based on probabilistic arguments. The main tools here are Brownian motion, stochastic calculus and Burkholder–Gundy inequalities for martingales. These methods allow us to improve somewhat our previous results, by proving that some significant constants do not depend on the dimension d.
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