Stochastic control
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Control theory for systems that move according to stochastic differential equations. Let B ( t ) be n- dimensional Brownian motion. The stochastic process U ( t ) that takes values in a given region Γ (called the control region) is called admissible control when the past part ( U (θ), B (θ), θ≦ t ) is independent of the Brownian motion increment B ( s ) - B ( t ). The motion when U ( t ) is used is given by the stochastic differential equation dX ( t )＝α( X ( t ), U ( t )) dB ( t )＋γ( X ( t ), U ( t )) dt . Source: Heibonsha World Encyclopedia, 2nd Edition Information |
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確率微分方程式に従って運動する系に対する制御理論。B(t)をn次元ブラウン運動とする。与えられた領域Γ(制御域という)の値をとる確率過程U(t)は，過去の部分(U(θ)，B(θ)，θ≦t)がブラウン運動の増分B(s)－B(t)とは独立のとき，許容されるコントロールと呼ばれる。U(t)を用いた場合の運動は確率微分方程式dX(t)＝α(X(t)，U(t))dB(t)＋γ(X(t)，U(t))dtで与えられる。
出典 株式会社平凡社世界大百科事典 第２版について 情報 |
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