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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Volume 287, Pages 129–139
DOI: https://doi.org/10.1134/S0371968514040086 (Mi tm3587) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On the submartingale/supermartingale property of diffusions in natural scale

Alexander Gushchina, Mikhail Urusovb, Mihail Zervosc

a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b Faculty of Mathematics, University of Duisburg-Essen, Essen, Germany
c Department of Mathematics, London School of Economics, London, UK
Full-text PDF (213 kB) Citations (6)
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DOI: https://doi.org/10.1134/S0371968514040086
Abstract: S. Kotani (2006) has characterised the martingale property of a one-dimensional diffusion in natural scale in terms of the classification of its boundaries. We complement this result by establishing a necessary and sufficient condition for a one-dimensional diffusion in natural scale to be a submartingale or a supermartingale. Furthermore, we study the asymptotic behaviour of the diffusion's expected state at time t as t→∞. We illustrate our results by means of several examples.
Funding agency Grant number
Russian Science Foundation 14-21-00162
The first and second authors were supported by the Russian Science Foundation, project no. 14-21-00162.
Received in August 2014
English version:
Proceedings of the Steklov Institute of Mathematics, 2014, Volume 287, Issue 1, Pages 122–132
DOI: https://doi.org/10.1134/S0081543814080082
Bibliographic databases:
Document Type: Article
UDC: 519.217
Language: English
Citation: Alexander Gushchin, Mikhail Urusov, Mihail Zervos, “On the submartingale/supermartingale property of diffusions in natural scale”, Stochastic calculus, martingales, and their applications, Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 287, MAIK Nauka/Interperiodica, Moscow, 2014, 129–139; Proc. Steklov Inst. Math., 287:1 (2014), 122–132
Citation in format AMSBIB
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\paper On the submartingale/supermartingale property of diffusions in natural scale
\inbook Stochastic calculus, martingales, and their applications
\bookinfo Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2014
\vol 287
\pages 129--139
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 6 articles:
    1. Ankirchner S., Kruse T., Urusov M., “Wasserstein Convergence Rates For Random BIT Approximations of Continuous Markov Processes”, J. Math. Anal. Appl., 493:2 (2021), 124543  crossref  mathscinet  isi  scopus
    2. A. Jacquier, M. Keller-Ressel, “Implied volatility in strict local martingale models”, SIAM J. Financ. Math., 9:1 (2018), 171–189  crossref  mathscinet  zmath  isi  scopus
    3. Yu. Shimizu, F. Nakano, “A remark on conditions that a diffusion in the natural scale is a martingale”, Osaka J. Math., 55:2 (2018), 385–391  mathscinet  zmath  isi
    4. M. Urusov, M. Zervos, “Necessary and sufficient conditions for the $r$-excessive local martingales to be martingales”, Electron. Commun. Probab., 22 (2017)  crossref  mathscinet  zmath  isi  scopus
    5. A. A. Gushchin, M. A. Urusov, “Processes that can be embedded in a geometric Brownian motion”, Theory Probab. Appl., 60:2 (2016), 246–262  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. D. Hobson, “Integrability of solutions of the Skorokhod embedding problem for diffusions”, Electron. J. Probab., 20 (2015), 83  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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