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Stochastic monotonicity and duality for one-dimensional Markov processes

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Abstract

The theory of monotonicity and duality is developed for general one-dimensional Feller processes, extending the approach from [1]. Moreover it is shown that local monotonicity conditions (conditions on the Lévy kernel) are sufficient to prove the well-posedness of the corresponding Markov semigroup and process, including unbounded coefficients and processes on the half-line.

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Authors and Affiliations

  1. Department of Statistics, University of Warwick, Warwick, UK

    V. N. Kolokol’tsov

  2. Moscow Economics Institute, Moscow, Russia

    V. N. Kolokol’tsov

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  1. V. N. Kolokol’tsov
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Correspondence to V. N. Kolokol’tsov.

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Published in Russian in Matematicheskie Zametki, 2011, Vol. 89, No. 5, pp. 694–704.

The text was submitted by the author in English.

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Kolokol’tsov, V.N. Stochastic monotonicity and duality for one-dimensional Markov processes. Math Notes 89, 652–660 (2011). https://doi.org/10.1134/S0001434611050063

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  • DOI: https://doi.org/10.1134/S0001434611050063

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