Opuscula Math. 38, no. 3 (2018), 307-326

Opuscula Mathematica

Backward stochastic variational inequalities driven by multidimensional fractional Brownian motion

Dariusz Borkowski
Katarzyna Jańczak-Borkowska

Abstract. We study the existence and uniqueness of the backward stochastic variational inequalities driven by \(m\)-dimensional fractional Brownian motion with Hurst parameters \(H_k\) (\(k=1,\ldots m\)) greater than \(1/2\). The stochastic integral used throughout the paper is the divergence type integral.

Keywords: backward stochastic differential equation, fractional Brownian motion, backward stochastic variational inequalities, subdifferential operator.

Mathematics Subject Classification: 60H05, 60H07, 60H22.

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  • Dariusz Borkowski
  • Nicolaus Copernicus University, Faculty of Mathematics and Computer Science, ul. Chopina 12/18, 87-100 Toruń, Poland
  • Katarzyna Jańczak-Borkowska
  • University of Science and Technology, Institute of Mathematics and Physics, al. prof. S. Kaliskiego 7, 85-796 Bydgoszcz, Poland
  • Communicated by Tomasz Zastawniak.
  • Received: 2017-03-07.
  • Revised: 2017-10-22.
  • Accepted: 2017-11-17.
  • Published online: 2018-03-19.
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Cite this article as:
Dariusz Borkowski, Katarzyna Jańczak-Borkowska, Backward stochastic variational inequalities driven by multidimensional fractional Brownian motion, Opuscula Math. 38, no. 3 (2018), 307-326, https://doi.org/10.7494/OpMath.2018.38.3.307

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