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Currents: The Stochastic Case

  • Vincenzo Capasso
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

We proceed here as for the deterministic case. At first we treat random distributions, with a particular attention to distributions associated with Radon measures. Special attention is devoted to random Radon measures associated with random closed sets, which is the basis of Stochastic Geometry. Later the general case of random m-currents is presented. Absolute continuity (in mean) is introduced, this being a concept of great importance in applications, as discussed in the relevant chapter. Two academic examples anticipate real applications; they concern an absolutely continuous 1-regular random set, and an absolutely continuous random 1-current, both related to a system of stochastic differential equations.

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Copyright information

© The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Vincenzo Capasso
    • 1
  1. 1.ADAMSS (Centre for Advanced Applied Mathematical and Statistical Sciences)Universitá degli Studi di Milano La StataleMilanoItaly

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