• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.9-23
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• 2018

In this paper, inspired by the fractional Brownian sheet of Riemann-Liouville type, we introduce the operator fractional Brownian sheet of Riemman-Liouville type, and study some properties of it. We also present an approximation in law to it based on the martingale differences.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.173-178
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• 2005

We derive an It${\hat{o}}$ formula for generalized functionals for the fractional Brownian sheet with arbitrary Hurst parameter ${H_1},\;H_2$ ${\epsilon}$ (0,1). As an application, we consider a stochastic integral representation for the local time of the fractional Brownian sheet.

• Communications for Statistical Applications and Methods
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• v.17 no.1
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• pp.47-54
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• 2010

By using the white noise theory for fractional Brownian sheet, we give new representations of the Wick integrals of various types with respect to fractional Brownian sheet with Hurst parameters $H_1,H_2{\in}$(0, 1).

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.479-489
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• 2019

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.

• Communications for Statistical Applications and Methods
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• v.19 no.3
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• pp.303-313
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• 2012

By using the techniques of a Malliavin calculus, we study the asymptotic behavior of the weighted cross-variation of a fractional Brownian sheet with a Hurst parameter $H=(H_1,H_2)$ such that 0 < $H_1$ < 1/2 and 0 < $H_1$ < 1/2.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.851-857
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• 2011

By using Malliavin calculus, we study a central limit theorem of the cross variation related to fractional Brownian sheet with Hurst parameter H = ($H_1$, $H_2$) such that 1/4 < $H_1$ < 1/2 and 1/4 < $H_2$ < 1/2.