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September 11, 2026
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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

International Journal of Dynamics and Control. 2025. Vol. 13. No. 5. Article 201.
Sergei Semakov

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.

Research target: Mathematics Computer Science
Language: English
DOI
Text on another site
Keywords: случайный процессвероятностьprobabilityцена акцииrandom processstock pricecrossing problemпересечение уровня
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