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The simple random walk { S n : n = 0, 1, …}, starting at an integer x, is a stochastic process on the integers, given by S 0 = x, S n = x + X 1 + … + X n ( n ≥ 1), where X n , n ≥ 1, is an independent Bernoulli sequence: P( X n = 1) = p, P( X n = −1) = 1 − p = q, 0 < p < 1.

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Random Walk

  • 工具书词条

  • 发表日期：

    2025年

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  • Rabi Bhattacharya

摘要

The simple random walk { S n : n = 0, 1, …}, starting at an integer x, is a stochastic process on the integers, given by S 0 = x, S n = x + X 1 + … + X n ( n ≥ 1), where X n , n ≥ 1, is an independent Bernoulli sequence: P( X n = 1) = p, P( X n = −1) = 1 − p = q, 0 < p < 1.