布朗運(yùn)動(dòng)及其應(yīng)用-文庫(kù)吧
2025-06-13 09:41 本頁(yè)面
【正文】 成，顯得非常沒(méi)規(guī)則而且其軌跡幾乎是處處沒(méi)有切線；粒子之移動(dòng)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(shí)也是如此；粒子越小或液體粘性越低或溫度越高時(shí)，粒子的運(yùn)動(dòng)越活潑；粒子的成分及密度對(duì)其運(yùn)動(dòng)沒(méi)有影響；粒子的運(yùn)動(dòng)永不停止。二．布朗運(yùn)動(dòng)在金融領(lǐng)域的發(fā)展1900年法國(guó)的巴施利葉在博士論文《投機(jī)理論》中將股票價(jià)格的漲跌也看作是一種隨機(jī)運(yùn)動(dòng)，所得到的方程與描述布朗粒子運(yùn)動(dòng)的方程非常相似。第一次給予布朗運(yùn)動(dòng)以嚴(yán)格的數(shù)學(xué)描述。但由此得到的股票價(jià)格可能取負(fù)值，顯然與實(shí)際不符當(dāng)然，巴施利葉所謂的“布朗運(yùn)動(dòng)”，實(shí)質(zhì)上指的是股市的價(jià)格變動(dòng)，換句話說(shuō)，他把股價(jià)的變動(dòng)，理想化為布朗運(yùn)動(dòng)．可見(jiàn)，在物理學(xué)界尚未把布朗運(yùn)動(dòng)研究清楚之前，它象征“無(wú)規(guī)行走的意義，早就被經(jīng)濟(jì)研究所吸納了。控制論創(chuàng)始人維納于1923年對(duì)布朗運(yùn)動(dòng)作出了嚴(yán)格的數(shù)學(xué)定義，根據(jù)這一定義，布朗運(yùn)動(dòng)是一種獨(dú)立增量過(guò)程，因而是一種馬爾科夫過(guò)程，數(shù)學(xué)界也常把布朗運(yùn)動(dòng)稱(chēng)為維納過(guò)程。Markowiz(1952)發(fā)表投資組合選擇理論；Roberts和Osborne(1959)把隨機(jī)數(shù)游走和布朗運(yùn)動(dòng)的概念帶入股市研究；Samuelson和Fama(1970)的有效市場(chǎng)理論(EMH)；FischerBlack和（BlackScholes模型）；Ross(1976)的套利定價(jià)理.布朗運(yùn)動(dòng)假設(shè)是現(xiàn)代資本市場(chǎng)理論的核心假設(shè)?，F(xiàn)代資本市場(chǎng)理論認(rèn)為證券期貨價(jià)格具有隨機(jī)性特征。這里的所謂隨機(jī)性，是指數(shù)據(jù)的無(wú)記憶性，即過(guò)去數(shù)據(jù)不構(gòu)成對(duì)未來(lái)數(shù)據(jù)的預(yù)測(cè)基礎(chǔ)。同時(shí)不會(huì)出現(xiàn)驚人相似的反復(fù)。股價(jià)行為模型通常用著名的維納過(guò)程來(lái)表達(dá)。假定股票價(jià)格遵循一般化的維納過(guò)程是很具誘惑力的，也就是說(shuō)，它具有不變的期望漂移率和方差率。將布朗運(yùn)動(dòng)與股票價(jià)格行為聯(lián)系在一起，進(jìn)而建立起維納過(guò)程的數(shù)學(xué)模型是本世紀(jì)的一項(xiàng)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(diǎn)仍認(rèn)為，股票市場(chǎng)是隨機(jī)波動(dòng)的。隨機(jī)波動(dòng)是股票市場(chǎng)最根本的特性，是股票市場(chǎng)的常態(tài)。布朗運(yùn)動(dòng)假設(shè)是現(xiàn)代資本市場(chǎng)理論的核心假設(shè)。現(xiàn)代資本市場(chǎng)理論認(rèn)為證券期貨價(jià)格具有隨機(jī)性特征。這里的所謂隨機(jī)性，是指數(shù)據(jù)的無(wú)記憶性，即過(guò)去數(shù)據(jù)不構(gòu)成對(duì)未來(lái)數(shù)據(jù)的預(yù)測(cè)基礎(chǔ)。同時(shí)不會(huì)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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