 In general, formula_34 has a modification that is a.s. continuous in formula_10 and càdlàg in formula_3.Tanaka's formula provides the explicit Doob–Meyer decomposition for the one-dimensional reflecting Brownian motion, formula_37.The field of local times formula_38 associated to a stochastic process on a space formula_39 is a well studied topic in the area of random fields.