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<p>We consider the problem of the exit of a diffusion Markov process to the boundary of a given domain. We concentrate on the one-dimensional case and solve the problem of finding the probability that the first exit of the process beyond the established corridor will occur at a given time. We apply the obtained results to the study of the behavior of the stock price when this behavior is described by the well-known model of Samuelson, according to which the relative change in price is the sum of the non-random trend and the Wiener process.</p>

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The problem of the exit of a random process to the boundary of a domain and its application to the study of the behavior of stock prices

  • 期刊论文

  • 发表日期：

    2025年5月12日

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  • Sergei Semakov

摘要

We consider the problem of the exit of a diffusion Markov process to the boundary of a given domain. We concentrate on the one-dimensional case and solve the problem of finding the probability that the first exit of the process beyond the established corridor will occur at a given time. We apply the obtained results to the study of the behavior of the stock price when this behavior is described by the well-known model of Samuelson, according to which the relative change in price is the sum of the non-random trend and the Wiener process.