…The theory of Brownian motion was further refined into a more beautiful mathematical form as an example of stochastic processes. It was developed by M. von Smoluchowski in Poland, Adriaan Daniël Fokker and M. Planck in Germany, and P. Langevin in France, and later by N. Wiener, it became a branch of the mathematics of stochastic processes. The Fokker-Planck equation is the equation that must be satisfied by the probability distribution function of the position and velocity of a particle, while the Langevin equation is the equation of motion of a particle, which includes a term for the damping of the velocity, an external force (gravity), and a fluctuating force as random noise. … *Some of the terminology that mentions "Fokker, AD" is listed below. Source | Heibonsha World Encyclopedia 2nd Edition | Information |
… ブラウン運動の理論はさらに,確率過程の例題として,より美しい数学的形式にみがき上げられていく。ポーランドのM.vonスモルコフスキー,ドイツのフォッカーAdriaan Daniël FokkerおよびM.プランク,フランスのP.ランジュバンによって発展され,さらにのちにはN.ウィーナーにより確率過程の数学の一部門にもなっていく。フォッカー=プランクの方程式は微粒子の位置と速度の確率分布関数がみたすべき方程式であり,ランジュバン方程式は微粒子の運動方程式で,速度の減衰項や外力(重力)のほかに,ランダム・ノイズとしてのゆらぐ力を含んでいる。… ※「Fokker,A.D.」について言及している用語解説の一部を掲載しています。 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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