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Weak solutions for stochastic differential equations with additive fractional noise

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  • Mishura, Yu.
  • Nualart, D.

Abstract

In this paper, we show the existence of a weak solution for a stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter , and a discontinuous drift. The proof of this result is based on the Girsanov theorem for the fractional Brownian motion.

Suggested Citation

  • Mishura, Yu. & Nualart, D., 2004. "Weak solutions for stochastic differential equations with additive fractional noise," Statistics & Probability Letters, Elsevier, vol. 70(4), pages 253-261, December.
    • Handle: RePEc:eee:stapro:v:70:y:2004:i:4:p:253-261
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    References listed on IDEAS

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    1. Nualart, David & Ouknine, Youssef, 2002. "Regularization of differential equations by fractional noise," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 103-116, November.
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    Cited by:

    1. Pauliina Ilmonen & Soledad Torres & Lauri Viitasaari, 2020. "Oscillating Gaussian processes," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 571-593, October.
    2. Azmoodeh Ehsan & Mishura Yuliya & Valkeila Esko, 2009. "On hedging European options in geometric fractional Brownian motion market model," Statistics & Risk Modeling, De Gruyter, vol. 27(02), pages 129-144, December.
    3. Hu, Yaozhong & Nualart, David & Song, Xiaoming, 2008. "A singular stochastic differential equation driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2075-2085, October.

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