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Absolute continuous approximations for multifractal processes and fields. (Ukrainian. English summary) Zbl 1249.60079

Summary: We define absolute continuous stochastic processes that converge to a multifractal Brownian motion in Besov-type spaces. The convergence of solutions of stochastic differential equations with such processes to a solution of the equation with multifractal Brownian motion is proved. Similar approximations are constructed in the case of two-parameter processes.

MSC:

60G22 Fractional processes, including fractional Brownian motion
60G60 Random fields
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