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1827年,英国生物学家布朗(R.Brown)观察到微小的粒子在液体(或气体)中不停地作极不规则的运动,这一发现在科学界产生了很大的影响。时间已经过去165年,关于这种运动的数学研究论文仍然层出不穷。国际上著名的几种概率论杂志中,几乎每期都有关于布朗运动的论文。1 一维布朗运动从发现到理论的建立经历了漫长的时间,其中有许多卓越人物的工作。1905年,爱因斯坦认为运动是由于微粒受到液体中大量分子的碰撞(每秒10~(20)次)而引起的。微粒在t时的位置x_t是随机的。假设x_0=0,以p(t,x)表x_t的一个坐标分量的分布密度,在一定条件下,他得到。
In 1827, the British biologist R. Brown observed that tiny particles constantly perform irregular movements in liquids (or gases). This discovery has had a great influence in the scientific community. The time has passed 165 years, and mathematics research papers about this kind of movement are still emerging. In several of the world’s most famous probabilistic journals, there are papers about Brown’s movement in almost every issue. 1 The one-dimensional Brownian movement has gone through a long period of time from the discovery to the establishment of the theory. Among them is the work of many outstanding figures. In 1905, Einstein believed that motion was caused by the collision of particles with a large number of molecules in the liquid (10 to 20 times per second). The position x_t of the particles at t is random. Assuming x_0=0, the distribution density of a coordinate component of x(t) in the p(t,x) table, under certain conditions, is obtained.