“random walk”的概念、定义、习题解题方法及翻译-数学辞典

单词

random walk

释义

random walk

With the integers positioned as they occur on the real line, imagine an object moving from integer to integer a step at a time. The position Xn of the object at the nth step is part of a Markov chain X1, X2, X3,…, with state space being the integers. Such a Markov chain is called a one-dimensional random walk if Xn = i, then Xn+1 = i −1, i or i + 1, so that the object may stay where it is, or move one to the left or right.

When a gambler, playing a sequence of games, either wins or loses a fixed amount in each game, their winnings give an example of a random walk, with 0 being an absorbing state.

Random walks in two or more dimensions can be defined similarly.

See Brownian motion.

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