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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:
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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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http://mi.mathnet.ru/eng/mz9121https://doi.org/10.4213/mzm9121 http://mi.mathnet.ru/eng/mz/v89/i5/p694
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:
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Kolokoltsov V., Lee R.X., “Stochastic Duality of Markov Processes: a Study via Generators”, Stoch. Anal. Appl., 31:6 (2013), 992–1023
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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
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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
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Sturm A., Swart J.M., “Pathwise Duals of Monotone and Additive Markov Processes”, J. Theor. Probab., 31:2 (2018), 932–983
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Baeumer B., Kovacs M., Sankaranarayanan H., “Fractional Partial Differential Equations With Boundary Conditions”, J. Differ. Equ., 264:2 (2018), 1377–1410
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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
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Foucart C., Ma Ch., Mallein B., “Coalescences in Continuous-State Branching Processes”, Electron. J. Probab., 24 (2019), 103
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