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In probability theory, reflected Brownian motion (or regulated Brownian motion,〔 both with the acronym RBM) is a Wiener process in a space with reflecting boundaries. RBMs have been shown to describe queueing models experiencing heavy traffic〔 as first proposed by Kingman and proven by Iglehart and Whitt. ==Definition== A ''d''–dimensional reflected Brownian motion ''Z'' is a stochastic process on uniquely defined by * a ''d''–dimensional drift vector ''μ'' * a ''d''×''d'' non-singular covariance matrix ''Σ'' and * a ''d''×''d'' reflection matrix ''R''. where ''X''(''t'') is an unconstrained Brownian motion and〔 :: with ''Y''(''t'') a ''d''–dimensional vector where * ''Y'' is continuous and non–decreasing with ''Y''(0) = 0 * ''Y''''j'' only increases at times for which ''Z''''j'' = 0 for ''j'' = 1,2,...,''d'' * ''Z''(''t'') ∈ S, t ≥ 0. The reflection matrix describes boundary behaviour. In the interior of the process behaves like a Wiener process, on the boundary "roughly speaking, ''Z'' is pushed in direction ''R''''j'' whenever the boundary surface is hit, where ''R''''j'' is the ''j''th column of the matrix ''R''."〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Reflected Brownian motion」の詳細全文を読む スポンサード リンク
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