Abstract:
We investigate the sufficient conditions for the strong and weak uniqueness of the solution of a stochastic equation with a simultaneous reflection at zero:
dxs=σ(s,xs)dws+b(s,xs)ds+dφs,dφs=χxs=0dφs,xs⩾0,
and for the existence of a strong solution of this equation.
Citation:
A. Ju. Veretennikov, “On the strong and weak solutions of one-dimensional stochastic equations with boundary conditions”, Teor. Veroyatnost. i Primenen., 26:4 (1981), 685–701; Theory Probab. Appl., 26:4 (1982), 670–686
\Bibitem{Ver81}
\by A.~Ju.~Veretennikov
\paper On the strong and weak solutions of one-dimensional stochastic equations with boundary conditions
\jour Teor. Veroyatnost. i Primenen.
\yr 1981
\vol 26
\issue 4
\pages 685--701
\mathnet{http://mi.mathnet.ru/tvp3500}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=636765}
\zmath{https://zbmath.org/?q=an:0499.60064}
\transl
\jour Theory Probab. Appl.
\yr 1982
\vol 26
\issue 4
\pages 670--686
\crossref{https://doi.org/10.1137/1126076}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1982PM42700002}
Linking options:
https://www.mathnet.ru/eng/tvp3500
https://www.mathnet.ru/eng/tvp/v26/i4/p685
This publication is cited in the following 12 articles:
Alexander Veretennikov, “Polynomial Recurrence for SDEs with a Gradient-Type Drift, Revisited”, Mathematics, 11:14 (2023), 3096
Mrinal K. Ghosh, Somnath Pradhan, “A nonzero-sum risk-sensitive stochastic differential game in the orthant”, MCRF, 12:2 (2022), 343
Somnath Pradhan, “Risk-Sensitive Ergodic Control of Reflected Diffusion Processes in Orthant”, Appl Math Optim, 83:3 (2021), 1739
Mrinal Kanti Ghosh, Somnath Pradhan, “Zero-sum risk-sensitive stochastic differential games with reflecting diffusions in the orthant”, ESAIM: COCV, 26 (2020), 114
O. A. Manita, A. Yu. Veretennikov, “O skhodimosti odnomernoi markovskoi diffuzii k statsionarnoi plotnosti s tyazhelymi khvostami”, Mosc. Math. J., 19:1 (2019), 89–106
Kazuhito Kawaguchi, Hiroaki Morimoto, “An Irreversible Investment Problem with Maintenance Expenditure”, SIAM J. Control Optim., 50:3 (2012), 1244
Arunabha Bagchi, K. Suresh Kumar, “Dynamic asset management with risk-sensitive criterion and non-negative factor constraints: a differential game approach”, Stochastics, 81:5 (2009), 503
M. Cristina Cerutti, Anna Piro Grimaldi, “Uniqueness for second-order parabolic equations with discontinuous coefficients”, Annali di Matematica, 186:1 (2007), 145
Veretennikov A.Y., “On lower bounds for mixing coefficients of Markov diffusions”, From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift, 2006, 623–633
A.Yu. Veretennikov, From Stochastic Calculus to Mathematical Finance, 2006, 623
Fulvio Gualtieri, Mario Giannella, Chemistry of Heterocyclic Compounds: A Series Of Monographs, 49, Chemistry of Heterocyclic Compounds, 1999, 1
A.Yu. Veretennikov, “On polynomial mixing bounds for stochastic differential equations”, Stochastic Processes and their Applications, 70:1 (1997), 115
Citation in format AMSBIB
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