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Applications of Mathematics

, Volume 63, Issue 1, pp 7–35 | Cite as

Stochastic Affine Evolution Equations with Multiplicative Fractional Noise

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Abstract

A stochastic affine evolution equation with bilinear noise term is studied, where the driving process is a real-valued fractional Brownian motion with Hurst parameter greater than 1/2. Stochastic integration is understood in the Skorokhod sense. The existence and uniqueness of weak solution is proved and some results on the large time dynamics are obtained.

Keywords

geometric fractional Brownian motion stochastic differential equations in Hilbert space stochastic bilinear equation 

MSC 2010

60H15 60G22 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsCharles UniversityPraha 8Czech Republic
  2. 2.Department of Mathematics, Faculty of Chemical EngineeringUniversity of Chemical Technology PraguePraha 6Czech Republic

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