Ren, Jiagang; Zhang, Hua Hypoellipticity and parabolic hypoellipticity of nonlocal operators under Hörmander’s condition. (English) Zbl 07749902 Potential Anal. 59, No. 3, 1051-1078 (2023). MSC: 60H07 60H10 PDFBibTeX XMLCite \textit{J. Ren} and \textit{H. Zhang}, Potential Anal. 59, No. 3, 1051--1078 (2023; Zbl 07749902) Full Text: DOI
Kirilov, Alexandre; De Moraes, Wagner A. A.; Ruzhansky, Michael Global properties of vector fields on compact Lie groups in Komatsu classes. II: Normal forms. (English) Zbl 1511.35358 Commun. Pure Appl. Anal. 21, No. 11, 3919-3940 (2022). MSC: 35R03 22E30 34C20 35H10 46F05 PDFBibTeX XMLCite \textit{A. Kirilov} et al., Commun. Pure Appl. Anal. 21, No. 11, 3919--3940 (2022; Zbl 1511.35358) Full Text: DOI arXiv
Hao, Zimo; Peng, Xuhui; Zhang, Xicheng Hörmander’s hypoelliptic theorem for nonlocal operators. (English) Zbl 1482.60072 J. Theor. Probab. 34, No. 4, 1870-1916 (2021). MSC: 60H07 60H10 60H30 PDFBibTeX XMLCite \textit{Z. Hao} et al., J. Theor. Probab. 34, No. 4, 1870--1916 (2021; Zbl 1482.60072) Full Text: DOI arXiv
Fernando, Kasun; Hebbar, Pratima Higher order asymptotics for large deviations. II. (English) Zbl 1475.60058 Stoch. Dyn. 21, No. 5, Article ID 2150025, 22 p. (2021). MSC: 60F10 60G51 60H10 PDFBibTeX XMLCite \textit{K. Fernando} and \textit{P. Hebbar}, Stoch. Dyn. 21, No. 5, Article ID 2150025, 22 p. (2021; Zbl 1475.60058) Full Text: DOI arXiv
Bally, Vlad; Caramellino, Lucia; Pigato, Paolo Tube estimates for diffusions under a local strong Hörmander condition. (English. French summary) Zbl 1434.60133 Ann. Inst. Henri Poincaré, Probab. Stat. 55, No. 4, 2320-2369 (2019). MSC: 60H07 60H10 60H30 PDFBibTeX XMLCite \textit{V. Bally} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 55, No. 4, 2320--2369 (2019; Zbl 1434.60133) Full Text: DOI arXiv Euclid
Bell, Denis Superdegenerate hypoelliptic differential operators. (English) Zbl 1415.60058 Budzban, Gregory (ed.) et al., Probability on algebraic and geometric structures. International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, Southern Illinois University, Carbondale, IL, USA, June 5–7, 2014. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 668, 13-20 (2016). MSC: 60H07 60H10 35H10 35R60 PDFBibTeX XMLCite \textit{D. Bell}, Contemp. Math. 668, 13--20 (2016; Zbl 1415.60058) Full Text: DOI Link
Lemaire, Vincent; Pagès, Gilles; Panloup, Fabien Invariant measure of duplicated diffusions and application to Richardson-Romberg extrapolation. (English. French summary) Zbl 1329.60281 Ann. Inst. Henri Poincaré, Probab. Stat. 51, No. 4, 1562-1596 (2015). MSC: 60J60 60J65 60F05 60H10 60H35 60G10 65C30 65C05 49Q20 PDFBibTeX XMLCite \textit{V. Lemaire} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 51, No. 4, 1562--1596 (2015; Zbl 1329.60281) Full Text: DOI arXiv Euclid
Mughetti, Marco On the spectrum of an anharmonic oscillator. (English) Zbl 1316.34090 Trans. Am. Math. Soc. 367, No. 2, 835-865 (2015). Reviewer: Manfred Möller (Johannesburg) MSC: 34L15 47E05 PDFBibTeX XMLCite \textit{M. Mughetti}, Trans. Am. Math. Soc. 367, No. 2, 835--865 (2015; Zbl 1316.34090) Full Text: DOI
Priola, Enrico On weak uniqueness for some degenerate SDEs by global \(L^p\) estimates. (English) Zbl 1306.60077 Potential Anal. 42, No. 1, 247-281 (2015). MSC: 60H10 60J60 PDFBibTeX XMLCite \textit{E. Priola}, Potential Anal. 42, No. 1, 247--281 (2015; Zbl 1306.60077) Full Text: DOI arXiv
Mughetti, Marco Parametrices for pseudodifferential operators with multiple characteristics. (English) Zbl 1347.47032 J. Pseudo-Differ. Oper. Appl. 5, No. 3, 343-358 (2014). Reviewer: Luigi Rodino (Torino) MSC: 47G30 34L15 PDFBibTeX XMLCite \textit{M. Mughetti}, J. Pseudo-Differ. Oper. Appl. 5, No. 3, 343--358 (2014; Zbl 1347.47032) Full Text: DOI
Bove, Antonio; Mughetti, Marco Analytic and Gevrey hypoellipticity for a class of pseudodifferential operators in one variable. (English) Zbl 1308.47056 J. Differ. Equations 255, No. 4, 728-758 (2013). Reviewer: Ioannis P. Stavroulakis (Ioannina) MSC: 47G30 PDFBibTeX XMLCite \textit{A. Bove} and \textit{M. Mughetti}, J. Differ. Equations 255, No. 4, 728--758 (2013; Zbl 1308.47056) Full Text: DOI
Hu, Yaozhong; Tindel, Samy Smooth density for some nilpotent rough differential equations. (English) Zbl 1277.60101 J. Theor. Probab. 26, No. 3, 722-749 (2013). MSC: 60H07 60H10 65C30 PDFBibTeX XMLCite \textit{Y. Hu} and \textit{S. Tindel}, J. Theor. Probab. 26, No. 3, 722--749 (2013; Zbl 1277.60101) Full Text: DOI arXiv
Hairer, Martin; Pillai, Natesh S. Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths. (English) Zbl 1288.60068 Ann. Probab. 41, No. 4, 2544-2598 (2013). Reviewer: Jan Gairing (Berlin) MSC: 60H07 26A33 35B65 60G10 60G22 60H10 PDFBibTeX XMLCite \textit{M. Hairer} and \textit{N. S. Pillai}, Ann. Probab. 41, No. 4, 2544--2598 (2013; Zbl 1288.60068) Full Text: DOI arXiv Euclid
Bakhtin, Yuri; Hurth, Tobias Invariant densities for dynamical systems with random switching. (English) Zbl 1251.93132 Nonlinearity 25, No. 10, 2937-2952 (2012). MSC: 93E15 93C30 37A50 PDFBibTeX XMLCite \textit{Y. Bakhtin} and \textit{T. Hurth}, Nonlinearity 25, No. 10, 2937--2952 (2012; Zbl 1251.93132) Full Text: DOI arXiv
Delarue, François; Menozzi, Stéphane Density estimates for a random noise propagating through a chain of differential equations. (English) Zbl 1223.60037 J. Funct. Anal. 259, No. 6, 1577-1630 (2010). Reviewer: D. R. Bell (Jacksonville) MSC: 60H10 PDFBibTeX XMLCite \textit{F. Delarue} and \textit{S. Menozzi}, J. Funct. Anal. 259, No. 6, 1577--1630 (2010; Zbl 1223.60037) Full Text: DOI
Nualart, David Malliavin calculus and its applications. (English) Zbl 1198.60006 CBMS Regional Conference Series in Mathematics 110. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4779-4/pbk). viii, 85 p. (2009). Reviewer: Michael Högele (Berlin) MSC: 60-02 60H07 60H05 60H10 PDFBibTeX XMLCite \textit{D. Nualart}, Malliavin calculus and its applications. Providence, RI: American Mathematical Society (AMS) (2009; Zbl 1198.60006)
Wihstutz, V. Nondegeneracy of the random double oscillator. (English) Zbl 1172.60323 ZAMM, Z. Angew. Math. Mech. 87, No. 11-12, 845-859 (2007). Reviewer: Eckhard Platen (Broadway) MSC: 60H10 60J65 35J70 PDFBibTeX XMLCite \textit{V. Wihstutz}, ZAMM, Z. Angew. Math. Mech. 87, No. 11--12, 845--859 (2007; Zbl 1172.60323) Full Text: DOI
Rey-Bellet, Luc Ergodic properties of Markov processes. (English) Zbl 1126.60057 Attal, Stéphane (ed.) et al., Open quantum systems II. The Markovian approach. Lecture notes of the summer school, Grenoble, France, June 16th – July 4th 2003. Berlin: Springer (ISBN 3-540-30992-6/pbk). Lecture Notes in Mathematics 1881, 1-39 (2006). Reviewer: Franco Fagnola (Milano) MSC: 60J25 60H10 60J60 82C31 PDFBibTeX XMLCite \textit{L. Rey-Bellet}, Lect. Notes Math. 1881, 1--39 (2006; Zbl 1126.60057) Full Text: DOI Link
Komatsu, T.; Takeuchi, Atsushi Generalized Hörmander theorem for non-local operators. (English) Zbl 1082.60045 Albeverio, Sergio (ed.) et al., Recent developments in stochastic analysis and related topics. Proceedings of the first Sino-German conference on stochastic analysis (a satellite conference of ICM 2002), Beijing, China, 29 August – 3 September 2002. River Edge, NJ: World Scientific (ISBN 981-256-104-8/hbk). 234-245 (2004). Reviewer: Bo Markussen (Kopenhagen) MSC: 60H07 60H10 60H30 60J60 60J75 PDFBibTeX XMLCite \textit{T. Komatsu} and \textit{A. Takeuchi}, in: Recent developments in stochastic analysis and related topics. Proceedings of the first Sino-German conference on stochastic analysis (a satellite conference of ICM 2002), Beijing, China, 29 August -- 3 September 2002. River Edge, NJ: World Scientific. 234--245 (2004; Zbl 1082.60045)
Filipović, Damir; Teichmann, Josef On the geometry of the term structure of interest rates. (English) Zbl 1048.60045 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 460, No. 2041, 129-167 (2004). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 60H10 58J65 91G30 PDFBibTeX XMLCite \textit{D. Filipović} and \textit{J. Teichmann}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 460, No. 2041, 129--167 (2004; Zbl 1048.60045) Full Text: DOI
Applebaum, David On a class of non-translation invariant Feller semigroups on Lie groups. (English) Zbl 1015.47027 Potential Anal. 16, No. 2, 103-114 (2002). Reviewer: Minping Qian (Beijing) MSC: 47D07 60B15 60J25 22E30 60H10 PDFBibTeX XMLCite \textit{D. Applebaum}, Potential Anal. 16, No. 2, 103--114 (2002; Zbl 1015.47027) Full Text: DOI
Pilipenko, A. Yu. Smoothness of distribution for solutions of SDE’s with interaction. (English) Zbl 1064.60142 Theory Stoch. Process. 7(23), No. 3-4, 113-117 (2001). Reviewer: Mikhail P. Moklyachuk (Kyïv) MSC: 60H10 60H07 60G30 PDFBibTeX XMLCite \textit{A. Yu. Pilipenko}, Theory Stoch. Process. 7(23), No. 3--4, 113--117 (2001; Zbl 1064.60142)
Shklyar, Alexander Some new effects for complete second order linear differential equations in Hilbert spaces. (English) Zbl 0965.34053 Ramm, A. G. (ed.) et al., Operator theory and its applications. Proceedings of the international conference, Winnipeg, Canada, October 7-11, 1998. Providence, RI: American Mathematical Society (AMS). Fields Inst. Commun. 25, 497-507 (2000). Reviewer: Stanislaw Wedrychowicz (Rzeszów) MSC: 34G10 47D09 47D06 34B40 47N20 PDFBibTeX XMLCite \textit{A. Shklyar}, in: Operator theory and its applications. Proceedings of the international conference, Winnipeg, Canada, October 7--11, 1998. Providence, RI: American Mathematical Society (AMS). 497--507 (2000; Zbl 0965.34053)
Yu, Ching-Chau Nonlinear eigenvalues and analytic-hypoellipticity. (English) Zbl 0913.35100 Mem. Am. Math. Soc. 636, 92 p. (1998). Reviewer: Niels Jacob (Erlangen) MSC: 35P20 35-02 34E20 65H10 35B65 PDFBibTeX XMLCite \textit{C.-C. Yu}, Nonlinear eigenvalues and analytic-hypoellipticity. Providence, RI: American Mathematical Society (AMS) (1998; Zbl 0913.35100) Full Text: DOI
Schiltz, Jang Hörmander’s theorem for degenerative second order differential operators with time dependent coefficients. (Le théorème de Hörmander pour des opérateurs du second ordre infiniment dégénérés avec des coefficients dépendant du temps.) (French) Zbl 0869.60049 Stochastics Stochastics Rep. 59, No. 3-4, 259-281 (1996). Reviewer: R.Buckdahn (Brest) MSC: 60H10 60H07 PDFBibTeX XMLCite \textit{J. Schiltz}, Stochastics Stochastics Rep. 59, No. 3--4, 259--281 (1996; Zbl 0869.60049) Full Text: DOI
Wihstutz, Volker Numerics of Lyapunov exponents of hypoelliptic linear stochastic systems. (English) Zbl 0852.65147 Kliemann, W. H. (ed.) et al., Nonlinear dynamics and stochastic mechanics. Proceedings of the international symposium, Waterloo, Canada, August 28–September 1, 1993. Providence, RI: American Mathematical Society. Fields Inst. Commun. 9, 203-217 (1996). MSC: 65C99 34F05 60H10 65L05 PDFBibTeX XMLCite \textit{V. Wihstutz}, Fields Inst. Commun. 9, 203--217 (1996; Zbl 0852.65147)
Gramchev, Todor; Yoshino, Masafumi WKB analysis to global solvability and hypoellipticity. (English) Zbl 0842.35021 Publ. Res. Inst. Math. Sci. 31, No. 3, 443-464 (1995). Reviewer: P.Popivanov (Sofia) MSC: 35H10 34E20 PDFBibTeX XMLCite \textit{T. Gramchev} and \textit{M. Yoshino}, Publ. Res. Inst. Math. Sci. 31, No. 3, 443--464 (1995; Zbl 0842.35021) Full Text: DOI
Bell, Denis R.; Mohammed, Salah-Eldin A. Degenerate stochastic differential equations, flows, and hypoellipticity. (English) Zbl 0826.60044 Cranston, Michael C. (ed.) et al., Stochastic analysis. Proceedings of the Summer Research Institute on stochastic analysis, held at Cornell University, Ithaca, NY, USA, July 11-30, 1993. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 57, 553-564 (1995). Reviewer: J.Franchi (Paris) MSC: 60H07 60H30 34K50 60H10 60H20 34F05 PDFBibTeX XMLCite \textit{D. R. Bell} and \textit{S.-E. A. Mohammed}, Proc. Symp. Pure Math. 57, 553--564 (1995; Zbl 0826.60044)
Fang, Shizan Quasi-sure analysis and estimation of the heat kernel for small times. (Analyse quasi-sure et l’estimation du noyau de la chaleur pour temps petit.) (French) Zbl 0782.60040 Trans. Am. Math. Soc. 339, No. 1, 221-241 (1993). Reviewer: N.Jacob (Erlangen) MSC: 60H07 58J65 60H10 PDFBibTeX XMLCite \textit{S. Fang}, Trans. Am. Math. Soc. 339, No. 1, 221--241 (1993; Zbl 0782.60040) Full Text: DOI
Florchinger, Patrick; Léandre, Rémi Estimation of the density of a strongly degenerated diffusion. Study of an example. (Estimation de la densité d’une diffusion très dégénérée. Étude d’un exemple.) (French) Zbl 0790.60049 J. Math. Kyoto Univ. 33, No. 1, 115-142 (1993). Reviewer: A.Yu.Veretennikov (Moskva) MSC: 60H07 60H10 PDFBibTeX XMLCite \textit{P. Florchinger} and \textit{R. Léandre}, J. Math. Kyoto Univ. 33, No. 1, 115--142 (1993; Zbl 0790.60049) Full Text: DOI
Chen, Hua Some problems related to totally characteristic operators. (Chinese. English summary) Zbl 0771.47027 J. Wuhan Univ., Nat. Sci. Ed. 1993, No. 1, 104-112 (1993). MSC: 47F05 47E05 58J05 PDFBibTeX XMLCite \textit{H. Chen}, J. Wuhan Univ., Nat. Sci. Ed. 1993, No. 1, 104--112 (1993; Zbl 0771.47027)
Cattiaux, Patrick Calcul stochastique et opérateurs dégénérés du second ordre. I: Résolvantes, théorème de Hörmander et applications. (Stochastic calculus and degenerated second order operators. I: Resolvents, theorem of Hörmander and applications). (French) Zbl 0715.60064 Bull. Sci. Math., II. Sér. 114, No. 4, 421-462 (1990). Reviewer: A.Yu.Veretennikov MSC: 60H07 60H10 60J60 60J35 65H10 35J25 35G15 PDFBibTeX XMLCite \textit{P. Cattiaux}, Bull. Sci. Math., II. Sér. 114, No. 4, 421--462 (1990; Zbl 0715.60064)
Nualart, D.; Sanz, M. Stochastic differential equations on the plane: Smoothness of the solution. (English) Zbl 0692.60044 J. Multivariate Anal. 31, No. 1, 1-29 (1989). Reviewer: M.Nisio MSC: 60H10 60H07 60G30 PDFBibTeX XMLCite \textit{D. Nualart} and \textit{M. Sanz}, J. Multivariate Anal. 31, No. 1, 1--29 (1989; Zbl 0692.60044) Full Text: DOI
Pinsky, M. A.; Wihstutz, Volker Lyapunov exponents of nilpotent Itô systems. (English) Zbl 0654.60043 Stochastics 25, No. 1, 43-57 (1988). MSC: 60H10 PDFBibTeX XMLCite \textit{M. A. Pinsky} and \textit{V. Wihstutz}, Stochastics 25, No. 1, 43--57 (1988; Zbl 0654.60043) Full Text: DOI
Ocone, Daniel L. A guide to the stochastic calculus of variations. (English) Zbl 0639.60060 Stochastic analysis and related topics, Proc. Workshop, Silivri/Turk., Lect. Notes Math. 1316, 1-79 (1988). Reviewer: M.Breger MSC: 60H07 60H10 65H10 PDFBibTeX XML
Norris, James Simplified Malliavin calculus. (English) Zbl 0609.60066 Probabilités XX, Proc. Sémin., Strasbourg 1984/85, Lect. Notes Math. 1204, 101-130 (1986). MSC: 60H10 60J60 60G30 60G46 PDFBibTeX XML Full Text: Numdam EuDML
Rodino, Luigi Tricomi function and other special functions in the study on the hypoellipticity. (English) Zbl 0601.35019 Mathematical analysis, Collect. works dedic. F. G. Tricomi, Teubner-Texte Math. 79, 203-219 (1985). Reviewer: K.Srivastava MSC: 35H10 PDFBibTeX XML
Kusuoka, S.; Stroock, D. Applications of the Malliavin calculus. II. (English) Zbl 0568.60059 J. Fac. Sci., Univ. Tokyo, Sect. I A 32, 1-76 (1985). Reviewer: M.Breger MSC: 60H10 60J60 65H10 58J65 PDFBibTeX XMLCite \textit{S. Kusuoka} and \textit{D. Stroock}, J. Fac. Sci., Univ. Tokyo, Sect. I A 32, 1--76 (1985; Zbl 0568.60059)
Michel, Dominique Conditional laws and Hörmander’s condition. (English) Zbl 0573.60035 Stochastic analysis, Proc. Taniguchi Int. Symp., Katata & Kyoto/Jap. 1982, North-Holland Math. Libr. 32, 387-408 (1984). Reviewer: M.Breger MSC: 60G35 93E11 60H10 65H10 PDFBibTeX XML
Kliemann, W. Transience, recurrence and invariant measures for diffusions. (English) Zbl 0518.60086 Nonlinear stochastic problems, Proc. NATO Adv. Study Inst., Armacao de Pera/Port. 1982, NATO ASI Ser., C, Math. Phys. Sci. 104, 437-454 (1983). MSC: 60J60 60H10 PDFBibTeX XML
Friedman, Avner Foundations of modern analysis. Reprint of the 1970 orig. (English) Zbl 0557.46001 New York: Dover Publications, Inc. VI, 250 p. (1982). MSC: 46-01 28-01 28A25 46B03 35D10 34B27 35J25 28A12 28A20 46B10 47B06 47B15 47A10 46E35 47B10 54E35 PDFBibTeX XML
Williams, David To begin at the beginning:…. (English) Zbl 0471.60065 Stochastic integrals, Proc. LMS Durham Symp. 1980, Lect. Notes Math. 851, 1-55 (1981). MSC: 60H10 58J65 PDFBibTeX XML
Bismut, Jean-Michel Martingales, the Malliavin calculus and Hörmander’s theorem. (English) Zbl 0457.60034 Stochastic integrals, Proc. LMS Durham Symp. 1980, Lect. Notes Math. 851, 85-109 (1981). MSC: 60H10 65H10 PDFBibTeX XML
Maire, H. M. Hypoelliptic overdetermined systems of partial differential equations. (English) Zbl 0436.35024 Commun. Partial Differ. Equations 5, 331-380 (1980). MSC: 35H10 35S05 35N99 PDFBibTeX XMLCite \textit{H. M. Maire}, Commun. Partial Differ. Equations 5, 331--380 (1980; Zbl 0436.35024) Full Text: DOI
De Gosson, Maurice Hypoellipticite partielle à la frontière des opérateurs pseudo- différentiels de transmission. (French) Zbl 0435.35087 Ann. Mat. Pura Appl., IV. Ser. 123, 377-402 (1980). MSC: 35S05 47F05 65H10 PDFBibTeX XMLCite \textit{M. De Gosson}, Ann. Mat. Pura Appl. (4) 123, 377--402 (1980; Zbl 0435.35087) Full Text: DOI
Malliavin, Paul Stochastic calculus of variation and hypoelliptic operators. (English) Zbl 0411.60060 Proc. int. Symp. on stochastic differential equations, Kyoto 1976, 195-263 (1978). MSC: 60H10 60B15 65H10 58J65 PDFBibTeX XML