Jia, Chen; Zhao, Guohuan Moderate maximal inequalities for the Ornstein-Uhlenbeck process. (English) Zbl 07211085 Proc. Am. Math. Soc. 148, No. 8, 3607-3615 (2020). MSC: 60H10 60J60 60J65 60G44 60E15 PDF BibTeX XML Cite \textit{C. Jia} and \textit{G. Zhao}, Proc. Am. Math. Soc. 148, No. 8, 3607--3615 (2020; Zbl 07211085) Full Text: DOI
Veraar, Mark; Yaroslavtsev, Ivan Pointwise properties of martingales with values in Banach function spaces. (English) Zbl 1443.60043 Gozlan, Nathael (ed.) et al., High dimensional probability VIII. The Oaxaca volume. Selected papers based on the presentations at the 8th conference on high-dimensional probability, HDP VIII, Casa Matemática Oaxaca (CMO), Mexico, May 28 – June 2, 2017. Cham: Birkhäuser. Prog. Probab. 74, 321-340 (2019). MSC: 60G44 60B11 60H05 60G48 PDF BibTeX XML Cite \textit{M. Veraar} and \textit{I. Yaroslavtsev}, Prog. Probab. 74, 321--340 (2019; Zbl 1443.60043) Full Text: DOI
Yaskov, Pavel A maximal inequality for fractional Brownian motions. (English) Zbl 1422.60067 J. Math. Anal. Appl. 472, No. 1, 11-21 (2019). MSC: 60G22 60E15 PDF BibTeX XML Cite \textit{P. Yaskov}, J. Math. Anal. Appl. 472, No. 1, 11--21 (2019; Zbl 1422.60067) Full Text: DOI
Siorpaes, Pietro Applications of pathwise Burkholder-Davis-Gundy inequalities. (English) Zbl 1407.60059 Bernoulli 24, No. 4B, 3222-3245 (2018). MSC: 60G44 60E15 60G40 60J60 PDF BibTeX XML Cite \textit{P. Siorpaes}, Bernoulli 24, No. 4B, 3222--3245 (2018; Zbl 1407.60059) Full Text: DOI Euclid arXiv
Ho, Kwok-Pun Martingale inequalities on rearrangement-invariant quasi-Banach function spaces. (English) Zbl 1399.60078 Acta Sci. Math. 83, No. 3-4, 619-627 (2017). Reviewer: Heinrich Hering (Rockenberg) MSC: 60G46 60G42 46E35 PDF BibTeX XML Cite \textit{K.-P. Ho}, Acta Sci. Math. 83, No. 3--4, 619--627 (2017; Zbl 1399.60078) Full Text: DOI
Veraar, Mark; Yaroslavtsev, Ivan Cylindrical continuous martingales and stochastic integration in infinite dimensions. (English) Zbl 1348.60081 Electron. J. Probab. 21, Paper No. 59, 53 p. (2016). MSC: 60H05 60B11 60G44 47D06 PDF BibTeX XML Cite \textit{M. Veraar} and \textit{I. Yaroslavtsev}, Electron. J. Probab. 21, Paper No. 59, 53 p. (2016; Zbl 1348.60081) Full Text: DOI Euclid arXiv
Beiglböck, Mathias; Siorpaes, Pietro Pathwise versions of the Burkholder-Davis-Gundy inequality. (English) Zbl 1352.60060 Bernoulli 21, No. 1, 360-373 (2015). Reviewer: Fraser Daly (Edinburgh) MSC: 60G42 60E15 60G46 91G20 PDF BibTeX XML Cite \textit{M. Beiglböck} and \textit{P. Siorpaes}, Bernoulli 21, No. 1, 360--373 (2015; Zbl 1352.60060) Full Text: DOI Euclid arXiv
Junge, Marius; Zeng, Qiang Noncommutative martingale deviation and Poincaré type inequalities with applications. (English) Zbl 1327.46062 Probab. Theory Relat. Fields 161, No. 3-4, 449-507 (2015). MSC: 46L53 60E15 47D06 PDF BibTeX XML Cite \textit{M. Junge} and \textit{Q. Zeng}, Probab. Theory Relat. Fields 161, No. 3--4, 449--507 (2015; Zbl 1327.46062) Full Text: DOI arXiv
Dirksen, Sjoerd Noncommutative Boyd interpolation theorems. (English) Zbl 1334.46019 Trans. Am. Math. Soc. 367, No. 6, 4079-4110 (2015). MSC: 46B70 46L52 46L53 PDF BibTeX XML Cite \textit{S. Dirksen}, Trans. Am. Math. Soc. 367, No. 6, 4079--4110 (2015; Zbl 1334.46019) Full Text: DOI arXiv
Yang, Minsuk A parabolic Triebel-Lizorkin space estimate for the fractional Laplacian operator. (English) Zbl 1318.42025 Proc. Am. Math. Soc. 143, No. 6, 2571-2578 (2015). Reviewer: Kôzô Yabuta (Nishinomiya) MSC: 42B25 42B35 60H15 46E35 60G51 26D10 PDF BibTeX XML Cite \textit{M. Yang}, Proc. Am. Math. Soc. 143, No. 6, 2571--2578 (2015; Zbl 1318.42025) Full Text: DOI arXiv
Cox, Sonja; Veraar, Mark Vector-valued decoupling and the Burkholder-Davis-Gundy inequality. (English) Zbl 1276.60017 Ill. J. Math. 55, No. 1, 343-375 (2011). Reviewer: Jacek Jakubowski (Warszawa) MSC: 60E15 60B11 60H05 46B09 PDF BibTeX XML Cite \textit{S. Cox} and \textit{M. Veraar}, Ill. J. Math. 55, No. 1, 343--375 (2011; Zbl 1276.60017) Full Text: Euclid arXiv
Li, Huiyun; Mu, Junfen; Li, Zhichan A generalization of the Burkholder-Davis-Gundy inequalities. (English) Zbl 1220.60015 Stochastics 83, No. 3, 233-240 (2011). MSC: 60E15 60G44 PDF BibTeX XML Cite \textit{H. Li} et al., Stochastics 83, No. 3, 233--240 (2011; Zbl 1220.60015) Full Text: DOI
Langovoy, Mikhail Algebraic polynomials and moments of stochastic integrals. (English) Zbl 1215.60036 Stat. Probab. Lett. 81, No. 6, 627-631 (2011). MSC: 60H05 60E15 60G44 33D45 26C10 62E20 PDF BibTeX XML Cite \textit{M. Langovoy}, Stat. Probab. Lett. 81, No. 6, 627--631 (2011; Zbl 1215.60036) Full Text: DOI arXiv
Matsui, Muneya; Shieh, Narn-Rueih On the exponentials of fractional Ornstein-Uhlenbeck processes. (English) Zbl 1191.60048 Electron. J. Probab. 14, 594-611 (2009). MSC: 60G22 60G17 60G15 60E15 PDF BibTeX XML Cite \textit{M. Matsui} and \textit{N.-R. Shieh}, Electron. J. Probab. 14, 594--611 (2009; Zbl 1191.60048) Full Text: DOI EMIS EuDML
Ren, Yanbo Some Orlicz-norm inequalities for martingales. (English) Zbl 1172.60011 Stat. Probab. Lett. 79, No. 9, 1238-1241 (2009). Reviewer: Ferenc Weisz (Budapest) MSC: 60G42 PDF BibTeX XML Cite \textit{Y. Ren}, Stat. Probab. Lett. 79, No. 9, 1238--1241 (2009; Zbl 1172.60011) Full Text: DOI
Peccati, Giovanni; Yor, Marc Burkholder’s submartingales from a stochastic calculus perspective. (English) Zbl 1176.60033 Ill. J. Math. 52, No. 3, 815-824 (2008). MSC: 60G44 60G15 PDF BibTeX XML Cite \textit{G. Peccati} and \textit{M. Yor}, Ill. J. Math. 52, No. 3, 815--824 (2008; Zbl 1176.60033) Full Text: Euclid
Parcet, Javier Weak type estimates associated to Burkholder’s martingale inequality. (English) Zbl 1155.46033 Rev. Mat. Iberoam. 23, No. 3, 1011-1037 (2007). Reviewer: Pavel Gapeev (London) MSC: 46L53 46L52 46L51 60G46 60G42 PDF BibTeX XML Cite \textit{J. Parcet}, Rev. Mat. Iberoam. 23, No. 3, 1011--1037 (2007; Zbl 1155.46033) Full Text: DOI Euclid EuDML arXiv
van Neerven, J. M. A. M.; Veraar, M. C.; Weis, L. Stochastic integration in UMD Banach spaces. (English) Zbl 1121.60060 Ann. Probab. 35, No. 4, 1438-1478 (2007). Reviewer: Kun Soo Chang (Seoul) MSC: 60H05 28C20 60B11 PDF BibTeX XML Cite \textit{J. M. A. M. van Neerven} et al., Ann. Probab. 35, No. 4, 1438--1478 (2007; Zbl 1121.60060) Full Text: DOI arXiv
Yan, Litan; Zhu, Bei \(L^p\)-estimates on diffusion processes. (English) Zbl 1064.60173 J. Math. Anal. Appl. 303, No. 2, 418-435 (2005). Reviewer: George Stoica (Saint John) MSC: 60J60 60G44 PDF BibTeX XML Cite \textit{L. Yan} and \textit{B. Zhu}, J. Math. Anal. Appl. 303, No. 2, 418--435 (2005; Zbl 1064.60173) Full Text: DOI
Yan, Litan Some ratio inequalities for iterated stochastic integrals. (English) Zbl 1035.60041 Math. Nachr. 259, 84-98 (2003). Reviewer: Pavel Gapeev (Moskva) MSC: 60G44 60H05 60J55 PDF BibTeX XML Cite \textit{L. Yan}, Math. Nachr. 259, 84--98 (2003; Zbl 1035.60041) Full Text: DOI
Yan, Litan On some inequalities of local times of iterated stochastic integrals. (English) Zbl 1019.60054 JIPAM, J. Inequal. Pure Appl. Math. 3, No. 4, Paper No. 62, 12 p. (2002). MSC: 60H05 60G44 60J55 PDF BibTeX XML Cite \textit{L. Yan}, JIPAM, J. Inequal. Pure Appl. Math. 3, No. 4, Paper No. 62, 12 p. (2002; Zbl 1019.60054) Full Text: Link EuDML
Yan, Litan An improved martingale inequality. (English) Zbl 1004.60056 Math. J. Toyama Univ. 24, 67-71 (2001). Reviewer: Klaus Schürger (Bonn) MSC: 60H05 60G44 PDF BibTeX XML Cite \textit{L. Yan}, Math. J. Toyama Univ. 24, 67--71 (2001; Zbl 1004.60056)
Choulli, Tahir; Stricker, Christophe; Krawczyk, Leszek On Fefferman and Burkholder-Davis-Gundy inequalities for \({\mathcal E}\)-martingales. (English) Zbl 0932.60050 Probab. Theory Relat. Fields 113, No. 4, 571-597 (1999). MSC: 60G48 60H05 91B28 PDF BibTeX XML Cite \textit{T. Choulli} et al., Probab. Theory Relat. Fields 113, No. 4, 571--597 (1999; Zbl 0932.60050) Full Text: DOI
Mishura, Yu. S.; Weisz, F. Atomic decompositions and inequalities for vector-valued discrete-time martingales. (English. Russian original) Zbl 0956.60037 Theory Probab. Appl. 43, No. 3, 487-496 (1998); translation from Teor. Veroyatn. Primen. 43, No. 3, 588-598 (1998). Reviewer: Ferenc Weisz (Budapest) MSC: 60G42 PDF BibTeX XML Cite \textit{Yu. S. Mishura} and \textit{F. Weisz}, Theory Probab. Appl. 43, No. 3, 487--496 (1998; Zbl 0956.60037); translation from Teor. Veroyatn. Primen. 43, No. 3, 588--598 (1998) Full Text: DOI
Brzeźniak, Zdzisław On Sobolev and Besov spaces regularity of Brownian paths. (English) Zbl 0890.60077 Stochastics Stochastics Rep. 56, No. 1-2, 1-15 (1996). Reviewer: K.Liubinskas (Vilnius) MSC: 60J65 60G17 PDF BibTeX XML Cite \textit{Z. Brzeźniak}, Stochastics Stochastics Rep. 56, No. 1--2, 1--15 (1996; Zbl 0890.60077) Full Text: DOI
Durrett, Richard Stochastic calculus. A practical introduction. (English) Zbl 0856.60002 Probability and Stochastics Series. Boca Raton, FL: CRC Press. vi, 341 p. (1996). Reviewer: M.Schweizer (Berlin) MSC: 60-01 60Hxx PDF BibTeX XML Cite \textit{R. Durrett}, Stochastic calculus. A practical introduction. Boca Raton, FL: CRC Press (1996; Zbl 0856.60002)
Tozoni, Sergio Antonio Weighted inequalities for vector operators on martingales. (English) Zbl 0843.60023 J. Math. Anal. Appl. 191, No. 2, 229-249 (1995). Reviewer: A.Gut (Uppsala) MSC: 60E15 60G42 PDF BibTeX XML Cite \textit{S. A. Tozoni}, J. Math. Anal. Appl. 191, No. 2, 229--249 (1995; Zbl 0843.60023) Full Text: DOI
Monat, P. Remarks on the Burkholder-Davis-Gundy inequalities. (Remarques sur les inégalités de Burkholder-Davis-Gundy.) (French) Zbl 0821.60053 Azéma, Jacques (ed.) et al., Séminaire de Probabilités XXVIII. Berlin: Springer-Verlag. Lect. Notes Math. 1583, 92-97 (1994). Reviewer: P.Vallois (Nancy) MSC: 60G44 60E15 PDF BibTeX XML Cite \textit{P. Monat}, Lect. Notes Math. 1583, 92--97 (1994; Zbl 0821.60053) Full Text: Numdam EuDML
Novikov, I. Ya. Martingale inequalities in rearrangement invariant spaces. (English. Russian original) Zbl 0843.60022 Sib. Math. J. 34, No. 1, 99-105 (1993); translation from Sib. Mat. Zh. 34, No. 1, 113-120 (1993). Reviewer: A.Gut (Uppsala) MSC: 60E15 60G42 PDF BibTeX XML Cite \textit{I. Ya. Novikov}, Sib. Math. J. 34, No. 1, 99--105 (1993; Zbl 0843.60022); translation from Sib. Mat. Zh. 34, No. 1, 113--120 (1993) Full Text: DOI
Roynette, Bernard Brownian motion and Besov spaces. (Mouvement brownien et espaces de Besov.) (French) Zbl 0808.60071 Stochastics Stochastics Rep. 43, No. 3-4, 221-260 (1993). Reviewer: S.Ogawa (Kyoto) MSC: 60J65 60J55 60F10 60H05 PDF BibTeX XML Cite \textit{B. Roynette}, Stochastics Stochastics Rep. 43, No. 3--4, 221--260 (1993; Zbl 0808.60071) Full Text: DOI
Long, Ruilin Martingale spaces and inequalities. (English) Zbl 0783.60047 Braunschweig: Vieweg. Beijing: Peking University Press. iv, 346 p. (1993). Reviewer: M.Scheutzow (Berlin) MSC: 60G42 60-02 60G46 PDF BibTeX XML Cite \textit{R. Long}, Martingale spaces and inequalities. Braunschweig: Vieweg; Beijing: Peking University Press (1993; Zbl 0783.60047)
Bassily, N. L. Duality of the Burkholder-Davis-Gundy inequality and the generalized Fefferman-Garsia inequality. II. (English) Zbl 0780.60042 Probability theory and applications, Essays to the Mem. of J. Mogyoródi, Math. Appl. 80, 33-45 (1992). Reviewer: M.Boutahar (Marseille) MSC: 60G42 60E15 PDF BibTeX XML Cite \textit{N. L. Bassily}, in: Probability theory and applications. Essays to the memory of József Mogyoródi. Dordrecht: Kluwer Academic Publishers. 33--45 (1992; Zbl 0780.60042)
Kallenberg, Olav; Sztencel, Rafał Some dimension-free features of vector-valued martingales. (English) Zbl 0717.60053 Probab. Theory Relat. Fields 88, No. 2, 215-247 (1991). Reviewer: O.Kallenberg MSC: 60G44 60G60 PDF BibTeX XML Cite \textit{O. Kallenberg} and \textit{R. Sztencel}, Probab. Theory Relat. Fields 88, No. 2, 215--247 (1991; Zbl 0717.60053) Full Text: DOI
Bassily, N. L. On two-sided inequalities for stopped random walks in Orlicz-spaces. (English) Zbl 0754.60007 Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 11, 63-73 (1991). MSC: 60B05 60G50 60E15 PDF BibTeX XML Cite \textit{N. L. Bassily}, Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 11, 63--73 (1991; Zbl 0754.60007)
Hitczenko, Paweł A remark on the paper “Martingale inequalities in rearrangement invariant function spaces” by W. B. Johnson and G. Schechtman. (English) Zbl 0804.60039 Functional analysis, Proc. Semin., Austin/TX (USA) 1987-89, Lect. Notes Math. 1470, 177-182 (1991). MSC: 60G44 60E15 PDF BibTeX XML
Gal’chuk, L. I. On the Lenglart and Burkholder-Davis-Gundy inequality for optional martingales. (Russian) Zbl 0714.60038 Statistics and control of stochastic processes, Collect. Artic., Moskva, 24-28 (1989). Reviewer: T.Bojdecki MSC: 60G44 60E15 PDF BibTeX XML
Schwartz, Laurent The convergence of the Picard series for stochastic differential equations. (La convergence de la série de Picard pour les EDS (équations différentielles stochastiques).) (French) Zbl 0743.60056 Séminaire de probabilités XXIII, Lect. Notes Math. 1372, 343-354 (1989). Reviewer: T.Bojdecki (Warszawa) MSC: 60H10 60E15 PDF BibTeX XML Full Text: Numdam EuDML
Bassily, N. L. A new proof of the right hand side of the Burkholder-Davis-Gundy inequality. (English) Zbl 0674.60047 Probability theory and mathematical statistics with applications, Proc. 5th Pannonian Symp., Visegrád/Hung. 1985, 7-21 (1988). Reviewer: M.P.Jerschow MSC: 60G42 PDF BibTeX XML
Bertoin, Jean Une extension d’une inégalité de Burkholder, Davis, Gundy pour les processus à \(\alpha\)-variation bornée et applications. (An extension of an inequality of Burkholder, Davis, Gundy for processes of bounded \(\alpha\)-variation and applications). (French) Zbl 0664.60023 Stochastics 24, No. 2, 75-86 (1988). Reviewer: J.Bertoin MSC: 60E15 PDF BibTeX XML Cite \textit{J. Bertoin}, Stochastics 24, No. 2, 75--86 (1988; Zbl 0664.60023) Full Text: DOI
Bassily, N. L. A proof of the left-hand side of the Burkholder-Davis-Gundy inequality for a large class of Orlicz spaces. (English) Zbl 0641.60054 Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Math. 30, 195-199 (1987). MSC: 60G42 60E15 46E30 PDF BibTeX XML Cite \textit{N. L. Bassily}, Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Math. 30, 195--199 (1987; Zbl 0641.60054)
Mishura, Yu. S. On properties of the quadratic variation of two-parameters strong martingales. (English) Zbl 0504.60051 Theory Probab. Math. Stat. 25, 99-106 (1982). MSC: 60G48 60G44 60H05 PDF BibTeX XML Cite \textit{Yu. S. Mishura}, Theory Probab. Math. Stat. 25, 99--106 (1982; Zbl 0504.60051)
Ikeda, Nobuyuki; Watanabe, Shinzo Stochastic differential equations and diffusion processes. (English) Zbl 0495.60005 North-Holland Mathematical Library, Vol. 24. Amsterdam - Oxford -New York: North-Holland Publishing Company. Tokyo: Kodansha Ltd. XIV, 464 p. $ 85.25; Dfl. 175.00 (1981). MSC: 60-02 PDF BibTeX XML
Mishura, Yu. S. On properties of the quadratic variation of two-parameter strong martingales. (Russian) Zbl 0469.60042 Teor. Veroyatn. Mat. Stat. 25, 92-99 (1981). MSC: 60G44 60H05 PDF BibTeX XML
Bichteler, Klaus Stochastic integration and \(L^ p-\)theory of semimartingales. (English) Zbl 0458.60057 Ann. Probab. 9, 49-89 (1981). MSC: 60H05 60H10 60G44 60J55 PDF BibTeX XML Cite \textit{K. Bichteler}, Ann. Probab. 9, 49--89 (1981; Zbl 0458.60057) Full Text: DOI
Dellacherie, Claude Inégalités de convexite pour les processus croissants et les sousmartingales. (French) Zbl 0416.60049 Seminaire de probabilites XIII, Univ. Strasbourg 1977/78, Lect. Notes Math. 721, 371-377 (1979). MSC: 60G44 60E15 PDF BibTeX XML Full Text: Numdam EuDML
Chevalier, Lucien Un nouveau type d’inégalités pour les martingales discretes. (English) Zbl 0393.60041 Z. Wahrscheinlichkeitstheor. Verw. Geb. 49, 249-255 (1979). MSC: 60G42 PDF BibTeX XML Cite \textit{L. Chevalier}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 49, 249--255 (1979; Zbl 0393.60041) Full Text: DOI