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Stochastics and Stochastic Reports Volume 75, 2003 - Issue 4
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Original Articles

Large deviations for multi-dimensional reflected fractional Brownian motion

Kurt MajewskiCorrespondence[email protected]
Pages 233-257 | Accepted 25 Nov 2002, Published online: 17 Oct 2011

Citations (15)

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Read on this site (2)

Kurt Majewski. (2007) Minimizing Large Deviation Paths for a Family of Long-Range Dependent Processes and Their Fractional Brownian Approximations. Stochastic Models 23:1, pages 49-77.
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Kurt Majewski. (2005) Sample path moderate deviations for a family of long-range dependent traffic and associated queue length processes. Stochastics 77:1, pages 81-107.
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Articles from other publishers (13)

Patrice Abry & Gustavo Didier. (2018) Wavelet estimation for operator fractional Brownian motion. Bernoulli 24:2.
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Martin Forde & Hongzhong Zhang. (2017) Asymptotics for Rough Stochastic Volatility Models. SIAM Journal on Financial Mathematics 8:1, pages 114-145.
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Chihoon Lee. (2016) A Geometric Drift Inequality for a Reflected Fractional Brownian Motion Process on the Positive Orthant. Journal of Applied Probability 48:3, pages 820-831.
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Chihoon Lee. (2016) A Geometric Drift Inequality for a Reflected Fractional Brownian Motion Process on the Positive Orthant. Journal of Applied Probability 48:03, pages 820-831.
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Gustavo Didier & Vladas Pipiras. (2011) Integral representations and properties of operator fractional Brownian motions. Bernoulli 17:1.
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Claudio Macci & Giovanni Luca Torrisi. (2011) Risk processes with shot noise Cox claim number process and reserve dependent premium rate. Insurance: Mathematics and Economics 48:1, pages 134-145.
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Ken R. Duffy & Sean P. Meyn. (2010) Most likely paths to error when estimating the mean of a reflected random walk. Performance Evaluation 67:12, pages 1290-1303.
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Kurt Majewski. (2009) Functional continuity and large deviations for the behavior of single-class queueing networks. Queueing Systems 61:2-3, pages 203-241.
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Kurt Majewski. (2016) Large deviation properties of constant rate data streams sharing a buffer with long-range dependent traffic in critical loading. Advances in Applied Probability 39:2, pages 407-428.
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Kurt Majewski. (2007) Sample path moderate deviations for the cumulative fluid produced by an increasing number of exponential on-off sources. Queueing Systems 56:1, pages 9-26.
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Kurt Majewski. (2006) Sample path large deviations for multiclass feedforward queueing networks in critical loading. The Annals of Applied Probability 16:4.
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Kurt Majewski. (2005) Fractional Brownian Heavy Traffic Approximations of Multiclass Feedforward Queueing Networks. Queueing Systems 50:2-3, pages 199-230.
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A.B. Dieker. (2005) Conditional limit theorems for queues with Gaussian input, a weak convergence approach. Stochastic Processes and their Applications 115:5, pages 849-873.
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