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In this paper a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.
Various paths properties of a stochastic process are obtained under mild conditions which allow for the integrability of the characteristic function of its increments and for the dependence among them. The main assumption is closely related to the notion of local asymptotic self-similarity. New results are obtained for the class of multifractional random(More)
We establish estimates for the local and uniform moduli of continuity of the local time of multifractional Brownian motion, B H = (B H(t) (t), t ∈ R +). An analogue of Chung's law of the iterated logarithm is studied for B H and used to obtain the pointwise Hölder exponent of the local time. A kind of local asymptotic self-similarity is proved to be(More)
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