布朗運動及其應(yīng)用-文庫吧
2025-06-13 09:41 本頁面
【正文】 成，顯得非常沒規(guī)則而且其軌跡幾乎是處處沒有切線；粒子之移動顯然互不相關(guān)，甚至于當(dāng)粒子互相接近至比其直徑小的距離時也是如此；粒子越小或液體粘性越低或溫度越高時，粒子的運動越活潑；粒子的成分及密度對其運動沒有影響；粒子的運動永不停止。二．布朗運動在金融領(lǐng)域的發(fā)展1900年法國的巴施利葉在博士論文《投機理論》中將股票價格的漲跌也看作是一種隨機運動，所得到的方程與描述布朗粒子運動的方程非常相似。第一次給予布朗運動以嚴(yán)格的數(shù)學(xué)描述。但由此得到的股票價格可能取負(fù)值，顯然與實際不符當(dāng)然，巴施利葉所謂的“布朗運動”，實質(zhì)上指的是股市的價格變動，換句話說，他把股價的變動，理想化為布朗運動．可見，在物理學(xué)界尚未把布朗運動研究清楚之前，它象征“無規(guī)行走的意義，早就被經(jīng)濟研究所吸納了?？刂普搫?chuàng)始人維納于1923年對布朗運動作出了嚴(yán)格的數(shù)學(xué)定義，根據(jù)這一定義，布朗運動是一種獨立增量過程，因而是一種馬爾科夫過程，數(shù)學(xué)界也常把布朗運動稱為維納過程。Markowiz(1952)發(fā)表投資組合選擇理論；Roberts和Osborne(1959)把隨機數(shù)游走和布朗運動的概念帶入股市研究；Samuelson和Fama(1970)的有效市場理論(EMH)；FischerBlack和（BlackScholes模型）；Ross(1976)的套利定價理.布朗運動假設(shè)是現(xiàn)代資本市場理論的核心假設(shè)?，F(xiàn)代資本市場理論認(rèn)為證券期貨價格具有隨機性特征。這里的所謂隨機性，是指數(shù)據(jù)的無記憶性，即過去數(shù)據(jù)不構(gòu)成對未來數(shù)據(jù)的預(yù)測基礎(chǔ)。同時不會出現(xiàn)驚人相似的反復(fù)。股價行為模型通常用著名的維納過程來表達。假定股票價格遵循一般化的維納過程是很具誘惑力的，也就是說，它具有不變的期望漂移率和方差率。將布朗運動與股票價格行為聯(lián)系在一起，進而建立起維納過程的數(shù)學(xué)模型是本世紀(jì)的一項具有重要意義的金融創(chuàng)新，在現(xiàn)代金融數(shù)學(xué)中占有重要地位。迄今，普遍的觀點仍認(rèn)為，股票市場是隨機波動的。隨機波動是股票市場最根本的特性，是股票市場的常態(tài)。布朗運動假設(shè)是現(xiàn)代資本市場理論的核心假設(shè)?，F(xiàn)代資本市場理論認(rèn)為證券期貨價格具有隨機性特征。這里的所謂隨機性，是指數(shù)據(jù)的無記憶性，即過去數(shù)據(jù)不構(gòu)成對未來數(shù)據(jù)的預(yù)測基礎(chǔ)。同時不會出現(xiàn)驚人相似的反復(fù)。英文翻譯：On the application of Brown in the financial fieldThe phenomenon of suspended particles never cease to do no regular movement is called Brown.For example, the observation of gamboge powder suspended in the water under the microscope, pollen grains, or in case of no observation of smoke in the air dust particle, will see this movement. The higher the temperature is, the more intense exercise. It is 1827 botanist R. Brown first discovered. Brown motion of the particle diameter is very small. 1~10 um, in the collision of surrounding liquid or gas molecules, the net force generated an irregular movement, Brown lead particles. If Brown particles collide with each other little chance can be regarded as the ideal gas giant molecules, then reach the heat balance in the gravity field, its number density according to the height of The distribution should follow the Boltzmann . Perrin experiments confirmed this point, and thus quite accurately measured A Fugadero constant and a series of related data and particle diffusion equation is established according to the Einstein A. statistical theory of Brown motion. Brown movement, experimental study and theoretical analysis indirectly confirmed no thermal motion of molecules, the kinetic theory of gases and confirm the atomic structure of the material is of great significance, and promote the development of statistical physics, especially the fluctuation theory. Due to the movement of Brown represents a random fluctuation, its theory for measuring precision Study on the limit and high magnification of background noise in the circuit of telemunications is widely used. This is the 1826 British botanist Brown (17731858) observed with a microscope found in the water suspen
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