23/11/26 18:11:22.91 EtUXTn+n.net
>>396
>数学的現象に対する興味を物理現象に対する興味と取り違えてますな
>数学的興味という動機を実用性の追求という動機と取り違えてますな
確率微分方程式/Stochastic differential equation/Itô calculus
1905年にAlbert Einsteinのブラウン運動の論文が出た
'Langevin' equationsが出て、1940年代に Kiyosi ItôのItô calculusが出た
つまり、物理 Albert Einsteinのブラウン運動の論文に触発されて
確率微分方程式→1940年代に Kiyosi ItôのItô calculus
もろ、物理の影響で”1940年代に Kiyosi ItôのItô calculus”が出た
それが、株式の理論に使われた
これが厳然たる事実です！
(参考)
URLﾘﾝｸ(ja.wikipedia.org)
確率微分方程式
URLﾘﾝｸ(en.wikipedia.org)
Stochastic differential equation
Background
Stochastic differential equations originated in the theory of Brownian motion, in the work of Albert Einstein and Marian Smoluchowski in 1905, although Louis Bachelier was the first person credited with modeling Brownian motion in 1900, giving a very early example of Stochastic Differential Equation now known as Bachelier model.
Some of these early examples were linear stochastic differential equations, also called 'Langevin' equations after French physicist Langevin, describing the motion of a harmonic oscillator subject to a random force. The mathematical theory of stochastic differential equations was developed in the 1940s through the groundbreaking work of Japanese mathematician Kiyosi Itô, who introduced the concept of stochastic integral and initiated the study of nonlinear stochastic differential equations. Another approach was later proposed by Russian physicist Stratonovich, leading to a calculus similar to ordinary calculus.
Terminology
Such a mathematical definition was first proposed by Kiyosi Itô in the 1940s, leading to what is known today as the Itô calculus.
The Itô integral and Stratonovich integral are related, but different, objects and the choice between them depends on the application considered. The Itô calculus is based on the concept of non-anticipativeness or causality, which is natural in applications where the variable is time.