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Mat. Zametki, 2011, Volume 89, Issue 5, Pages 694–704 (Mi mz9121)  

This article is cited in 7 scientific papers (total in 7 papers)

Stochastic Monotonicity and Duality for One-Dimensional Markov Processes

V. N. Kolokoltsovab

a University of Warwick, United Kingdom
b Moscow Economical Institute

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.

Keywords: stochastic monotonicity, duality, one-dimensional Markov process, Lévy–Kchintchine type generator

DOI: https://doi.org/10.4213/mzm9121

Full text: PDF file (487 kB)
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English version:
Mathematical Notes, 2011, 89:5, 652–660

Bibliographic databases:

UDC: 519.248
Received: 17.05.2010
Revised: 11.12.2010

Citation: V. N. Kolokoltsov, “Stochastic Monotonicity and Duality for One-Dimensional Markov Processes”, Mat. Zametki, 89:5 (2011), 694–704; Math. Notes, 89:5 (2011), 652–660

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kolokoltsov V., Lee R.X., “Stochastic Duality of Markov Processes: a Study via Generators”, Stoch. Anal. Appl., 31:6 (2013), 992–1023  crossref  mathscinet  zmath  isi  scopus
    2. Kolokoltsov V., “on Fully Mixed and Multidimensional Extensions of the Caputo and Riemann-Liouville Derivatives, Related Markov Processes and Fractional Differential Equations”, Fract. Calc. Appl. Anal., 18:4 (2015), 1039–1073  crossref  mathscinet  zmath  isi  elib  scopus
    3. Kolokoltsov V.N., “Stochastic Monotonicity and Duality of Kth Order With Application To Put-Call Symmetry of Powered Options”, J. Appl. Probab., 52:1 (2015), 82–101  crossref  mathscinet  zmath  isi  elib
    4. Sturm A., Swart J.M., “Pathwise Duals of Monotone and Additive Markov Processes”, J. Theor. Probab., 31:2 (2018), 932–983  crossref  mathscinet  isi  scopus
    5. Baeumer B., Kovacs M., Sankaranarayanan H., “Fractional Partial Differential Equations With Boundary Conditions”, J. Differ. Equ., 264:2 (2018), 1377–1410  crossref  mathscinet  zmath  isi  scopus
    6. Goffard P.-O., Sarantsev A., “Exponential Convergence Rate of Ruin Probabilities For Level-Dependent Levy-Driven Risk Processes”, J. Appl. Probab., 56:4 (2019), PII S0021900219000718, 1244–1268  crossref  mathscinet  isi
    7. Foucart C., Ma Ch., Mallein B., “Coalescences in Continuous-State Branching Processes”, Electron. J. Probab., 24 (2019), 103  crossref  mathscinet  isi
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