Opuscula Math. 38, no. 3 (2018), 307-326
https://doi.org/10.7494/OpMath.2018.38.3.307

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.
• Revised: 2017-10-22.
• Accepted: 2017-11-17.
• Published online: 2018-03-19.