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Almost periodic solutions in distribution to affine stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2

Authors
  • Akeb, Tassadit
  • Challali, Nordine
  • Mellah, Omar
Publication Date
Oct 04, 2020
Source
HAL-Descartes
Keywords
Language
English
License
Unknown
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Abstract

The few works devoted to the existence of almost periodicity (or almost automorphy) solutions to stochastic differential equations driven by a fractional Brownian motion impose the condition: the coefficient of fractional stochastic part is deterministic. In this work, without this condition, by using the chaos decomposition approach and the representation of the fractional Brownian motion in terms of a standard Brownian motion, we obtain the existence and uniqueness of almost periodic solution in distribution to affine stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H > 1 2 .

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