Random Walks and Stochastic Differential Equations
Random Walks and Stochastic Differential Equations
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随机游走和随机微分方程
DOI：
10.1007/978-1-4615-5823-1_3
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
C. Tapiero
中科院分区：
文献类型：
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作者：
C. Tapiero
随机过程是一对{x，t≥0}或也记为x(T)，其中f(x，t)表示过程时间路径呈现实值的概率分布。对随机过程的研究起源于19世纪物理学家对气体中分子运动行为的研究。直到本世纪，在爱因斯坦、科尔莫戈罗夫、利维、维纳等人的工作之后，人们才对随机过程进行了一些深入的研究。巴谢里耶在1900年的论文中已经对股票交易投机进行了研究，建立了股票交易中的价格波动和布朗运动之间的联系，布朗运动是本文要研究的一类重要的随机过程。此外，巴舍利耶还构建了公平博弈的数学模型，也就是我们在第二章附录中看到的，也就是我们将在第四章中看到的鞅。
A stochastic process is a pair {x,t≥ 0} or also writtenx(t) withf(x,t) denoting the probability distribution that the process time path assumes a real valuexat timet. The study of stochastic processes has its origin in the study of kinetic behaviour of molecules in gas by physicists in the 19th century. It is only in this century, following works by Einstein, Kolmogorov, Levy, Wiener and others that stochastic processes have been studied in some depth. Bachelier, already in his dissertation in 1900 provided a study of stock exchange speculation establishing a connection between price fluctuations in the stock exchange and Brownian motion, an important class of stochastic processes to be studied here. In addition, Bachelier constructed the mathematical model for a fair game, or the martingale as we saw in the appendix in Chapter 2 and as we shall see in Chapter 4.