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On a Sufficient Condition for a Diffusion Process Will Never Reach Boundaries of Some Interval

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A one-dimensional diffusion semi-Markov process on some interval of its values is considered. Semi-Markov transition functions of the process satisfy a second order differential equation with coefficients admitting possibility that the process stops inside this interval. In terms of coefficients of this equation, some sufficient conditions are proved for the process will neither reach the left or right boundaries of this interval.

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Authors and Affiliations

  1. Institute of Problems of Mechanical Engineering, St.Petersburg, Russia

    B. P. Harlamov

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  1. B. P. Harlamov
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Correspondence to B. P. Harlamov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 495, 2020, pp. 291–304.

Translated by I. Ponomarenko.

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Harlamov, B.P. On a Sufficient Condition for a Diffusion Process Will Never Reach Boundaries of Some Interval. J Math Sci 268, 721–730 (2022). https://doi.org/10.1007/s10958-022-06243-7

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  • DOI: https://doi.org/10.1007/s10958-022-06243-7

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