Abstract
We study renormalized self-intersection local times γ n ( μ x ; t) for Lévy processes, where the n-fold multiple points are weighted by the translate μ x of an arbitrary measure μ. General sufficient conditions are provided which insure that γ n ( μ x ; t) is a.s. jointly continuous in x and t. Our proof involves a new Doob-Meyer type decomposition of γ n ( μ x ; t) as the difference of a martingale and a lower order renormalized self-intersection local time.
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