Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2019; 56(2): 479-489

Online first article October 24, 2018      Printed March 1, 2019

https://doi.org/10.4134/BKMS.b180345

Copyright © The Korean Mathematical Society.

Stochastic differential equations driven by an additive fractional Brownian sheet

Oussama El Barrimi, Youssef Ouknine

Cadi Ayyad University; Mohammed VI polytechnic University Ben Ghuerir

Abstract

In this paper, we show the existence of a weak solution for a stochastic differential equation driven by an additive fractional Brownian sheet with Hurst parameters $H,H' > 1/2$, and a drift coefficient satisfying the linear growth condition. The result is obtained using a suitable Girsanov theorem for the fractional Brownian sheet.

Keywords: fractional Brownian sheet, stochastic differential equations, weak solutions

MSC numbers: 60G22, 60G15