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2 | I TeXed the mathematics. | ||
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From the Markov property of the random walk (X_n) $(X_n)$ we have P(X_4>0 $$P(X_4>0 \ |\ X_3>0, X_2>0) = P(X_4>0\ |X_3>0).\ X_3>0).$$ To paraphrase Kai Lai Chung in his book "Green, Brown, and Probability", "The Markov property means that the past has no after-effect on the future when the present is known; but beware, big mistakes have been made through misunderstanding the exact meaning of the words "when the present is known"." |
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1 | [made Community Wiki] | ||
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From the Markov property of the random walk (X_n) we have P(X_4>0 | X_3>0, X_2>0) = P(X_4>0 | X_3>0). To paraphrase Kai Lai Chung in his book "Green, Brown, and Probability", "The Markov property means that the past has no after-effect on the future when the present is known; but beware, big mistakes have been made through misunderstanding the exact meaning of the words "when the present is known"." |
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