Abstract
Let W( t) be a standard Wiener process with local time L( x, t). It is well-known that, as stochastic processes, L(0, t) and sup o ⩽ s ⩽ t W( s) have the same distribution (Lévy, 1939). Here we give a new derivation of the distribution of L( x, t + h) − L( x, t) for each x ∈ R 1, t, h ⩾ 0 .
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