Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi; Wang, Jian Two-sided heat kernel estimates for symmetric diffusion processes with jumps: recent results. (English) Zbl 1497.60110 Chen, Zhen-Qing (ed.) et al., Dirichlet forms and related topics, in honor of Masatoshi Fukushima’s beiju, IWDFRT 2022, Osaka, Japan, August 22–26,2022. Singapore: Springer. Springer Proc. Math. Stat. 394, 63-83 (2022). MSC: 60J60 60J35 60J76 31C25 60J45 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., Springer Proc. Math. Stat. 394, 63--83 (2022; Zbl 1497.60110) Full Text: DOI
Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian Heat kernel estimates for general symmetric pure jump Dirichlet forms. (English) Zbl 1506.60080 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 23, No. 3, 1091-1140 (2022). Reviewer: Nicolas Privault (Singapura) MSC: 60J35 35K08 60J76 31C25 60J25 60J45 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 23, No. 3, 1091--1140 (2022; Zbl 1506.60080) Full Text: DOI arXiv
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi; Wang, Jian Heat kernels for reflected diffusions with jumps on inner uniform domains. (English) Zbl 1498.60321 Trans. Am. Math. Soc. 375, No. 10, 6797-6841 (2022). MSC: 60J35 60J76 31C25 35K08 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., Trans. Am. Math. Soc. 375, No. 10, 6797--6841 (2022; Zbl 1498.60321) Full Text: DOI arXiv
Kassmann, Moritz; Kim, Kyung-Youn; Kumagai, Takashi Heat kernel bounds for nonlocal operators with singular kernels. (English. French summary) Zbl 1493.60122 J. Math. Pures Appl. (9) 164, 1-26 (2022). Reviewer: Rodica Luca (Iaşi) MSC: 60J74 35K08 47G20 PDFBibTeX XMLCite \textit{M. Kassmann} et al., J. Math. Pures Appl. (9) 164, 1--26 (2022; Zbl 1493.60122) Full Text: DOI arXiv
Chen, Xin; Chen, Zheng-Qing; Kumagai, Takashi; Wang, Jian Homogenization of symmetric jump processes in random media. (English) Zbl 1513.60051 Rev. Roum. Math. Pures Appl. 66, No. 1, 83-105 (2021). MSC: 60G51 60G52 60J25 60J76 PDFBibTeX XMLCite \textit{X. Chen} et al., Rev. Roum. Math. Pures Appl. 66, No. 1, 83--105 (2021; Zbl 1513.60051) Full Text: Link
Chen, Xin; Kumagai, Takashi; Wang, Jian Random conductance models with stable-like jumps: quenched invariance principle. (English) Zbl 1479.60095 Ann. Appl. Probab. 31, No. 3, 1180-1231 (2021). MSC: 60G51 60F17 60G52 60J25 60J76 PDFBibTeX XMLCite \textit{X. Chen} et al., Ann. Appl. Probab. 31, No. 3, 1180--1231 (2021; Zbl 1479.60095) Full Text: DOI arXiv Link
Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian Stability of heat kernel estimates and parabolic Harnack inequalities for general symmetric pure jump processes. (English) Zbl 1479.60158 Grigor’yan, Alexander (ed.) et al., Analysis and partial differential equations on manifolds, fractals and graphs. Contributions of the conference, Tianjin, China, September 2019. Berlin: De Gruyter. Adv. Anal. Geom. 3, 3-25 (2021). Reviewer: Weiping Li (Guanghan) MSC: 60J35 35K08 60J76 31C25 60J25 60J45 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., Adv. Anal. Geom. 3, 3--25 (2021; Zbl 1479.60158) Full Text: DOI
Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian Stability of heat kernel estimates for symmetric non-local Dirichlet forms. (English) Zbl 1498.60007 Memoirs of the American Mathematical Society 1330. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4863-9/pbk; 978-1-4704-6638-1/ebook). v, 89 p. (2021). MSC: 60-02 60J35 35K08 60J76 31C25 60J25 60J45 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., Stability of heat kernel estimates for symmetric non-local Dirichlet forms. Providence, RI: American Mathematical Society (AMS) (2021; Zbl 1498.60007) Full Text: DOI arXiv
Biskup, Marek; Chen, Xin; Kumagai, Takashi; Wang, Jian Quenched invariance principle for a class of random conductance models with long-range jumps. (English) Zbl 1472.60059 Probab. Theory Relat. Fields 180, No. 3-4, 847-889 (2021). MSC: 60F17 60J45 60G50 60J76 PDFBibTeX XMLCite \textit{M. Biskup} et al., Probab. Theory Relat. Fields 180, No. 3--4, 847--889 (2021; Zbl 1472.60059) Full Text: DOI arXiv
Chen, Xin; Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian Homogenization of symmetric stable-like processes in stationary ergodic media. (English) Zbl 1481.60089 SIAM J. Math. Anal. 53, No. 3, 2957-3001 (2021). MSC: 60G51 60G52 60J25 60J76 PDFBibTeX XMLCite \textit{X. Chen} et al., SIAM J. Math. Anal. 53, No. 3, 2957--3001 (2021; Zbl 1481.60089) Full Text: DOI arXiv
Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms. (English) Zbl 1455.35004 J. Eur. Math. Soc. (JEMS) 22, No. 11, 3747-3803 (2020). Reviewer: Vincenzo Vespri (Firenze) MSC: 35A23 35B51 35B35 35B65 60J76 28A80 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., J. Eur. Math. Soc. (JEMS) 22, No. 11, 3747--3803 (2020; Zbl 1455.35004) Full Text: DOI arXiv Backlinks: MO
Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms. (English) Zbl 1471.60118 Adv. Math. 374, Article ID 107269, 71 p. (2020). MSC: 60J35 35K08 60J60 60J76 31C25 60J25 60J45 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., Adv. Math. 374, Article ID 107269, 71 p. (2020; Zbl 1471.60118) Full Text: DOI arXiv
Chen, Xin; Kumagai, Takashi; Wang, Jian Random conductance models with stable-like jumps: heat kernel estimates and Harnack inequalities. (English) Zbl 1459.60213 J. Funct. Anal. 279, No. 7, Article ID 108656, 50 p. (2020). MSC: 60K37 60G50 60K35 60F17 60J76 PDFBibTeX XMLCite \textit{X. Chen} et al., J. Funct. Anal. 279, No. 7, Article ID 108656, 50 p. (2020; Zbl 1459.60213) Full Text: DOI arXiv
Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian Elliptic Harnack inequalities for symmetric non-local Dirichlet forms. (English. French summary) Zbl 1415.35069 J. Math. Pures Appl. (9) 125, 1-42 (2019). Reviewer: Vincenzo Vespri (Firenze) MSC: 35B51 35B65 28A80 60J75 35B20 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., J. Math. Pures Appl. (9) 125, 1--42 (2019; Zbl 1415.35069) Full Text: DOI arXiv Link
Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian Mean value inequalities for jump processes. (English) Zbl 1405.60116 Eberle, Andreas (ed.) et al., Stochastic partial differential equations and related fields. In honor of Michael Röckner, SPDERF, Bielefeld, Germany, October 10–14, 2016. Cham: Springer (ISBN 978-3-319-74928-0/hbk; 978-3-319-74929-7/ebook). Springer Proceedings in Mathematics & Statistics 229, 421-437 (2018). MSC: 60J35 31B05 60J75 31C25 35K08 60J45 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., Springer Proc. Math. Stat. 229, 421--437 (2018; Zbl 1405.60116) Full Text: DOI
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi; Wang, Jian Heat kernel estimates for time fractional equations. (English) Zbl 1401.60088 Forum Math. 30, No. 5, 1163-1192 (2018). MSC: 60G52 60J25 60J55 60J35 60J75 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., Forum Math. 30, No. 5, 1163--1192 (2018; Zbl 1401.60088) Full Text: DOI arXiv
Kim, Panki; Kumagai, Takashi; Wang, Jian Laws of the iterated logarithm for symmetric jump processes. (English) Zbl 1407.60114 Bernoulli 23, No. 4A, 2330-2379 (2017). MSC: 60J75 60F05 PDFBibTeX XMLCite \textit{P. Kim} et al., Bernoulli 23, No. 4A, 2330--2379 (2017; Zbl 1407.60114) Full Text: DOI arXiv Euclid
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi Corrigendum to: “Global heat kernel estimates for symmetric jump processes”. (English) Zbl 1330.60102 Trans. Am. Math. Soc. 367, No. 10, 7515 (2015). MSC: 60J75 31B05 31C25 60J35 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., Trans. Am. Math. Soc. 367, No. 10, 7515 (2015; Zbl 1330.60102) Full Text: DOI
Bogdan, Krzysztof; Kumagai, Takashi; Kwaśnicki, Mateusz Boundary Harnack inequality for Markov processes with jumps. (English) Zbl 1309.60080 Trans. Am. Math. Soc. 367, No. 1, 477-517 (2015). Reviewer: Oleg K. Zakusilo (Kyïv) MSC: 60J50 60J75 31B05 60G51 60J65 PDFBibTeX XMLCite \textit{K. Bogdan} et al., Trans. Am. Math. Soc. 367, No. 1, 477--517 (2015; Zbl 1309.60080) Full Text: DOI arXiv
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi Discrete approximation of symmetric jump processes on metric measure spaces. (English) Zbl 1274.60238 Probab. Theory Relat. Fields 155, No. 3-4, 703-749 (2013). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 60J25 60B10 60J75 60G52 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., Probab. Theory Relat. Fields 155, No. 3--4, 703--749 (2013; Zbl 1274.60238) Full Text: DOI arXiv
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi Global heat kernel estimates for symmetric jump processes. (English) Zbl 1234.60088 Trans. Am. Math. Soc. 363, No. 9, 5021-5055 (2011); corrigendum ibid. 367, No. 10, 7515 (2015). Reviewer: Zoran Vondraček (Zagreb) MSC: 60J75 31B05 31C25 60J35 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., Trans. Am. Math. Soc. 363, No. 9, 5021--5055 (2011; Zbl 1234.60088) Full Text: DOI
Chen, Zhen-Qing; Kumagai, Takashi A priori Hölder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps. (English) Zbl 1200.60065 Rev. Mat. Iberoam. 26, No. 2, 551-589 (2010). Reviewer: Liliana Popa (Iaşi) MSC: 60J35 47G30 60J45 31C05 31C25 60J75 PDFBibTeX XMLCite \textit{Z.-Q. Chen} and \textit{T. Kumagai}, Rev. Mat. Iberoam. 26, No. 2, 551--589 (2010; Zbl 1200.60065) Full Text: DOI arXiv Euclid
Bass, Richard F.; Kassmann, Moritz; Kumagai, Takashi Symmetric jump processes: localization, heat kernels and convergence. (English) Zbl 1201.60078 Ann. Inst. Henri Poincaré, Probab. Stat. 46, No. 1, 59-71 (2010). Reviewer: Liliana Popa (Iaşi) MSC: 60J35 60J75 45K05 PDFBibTeX XMLCite \textit{R. F. Bass} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 46, No. 1, 59--71 (2010; Zbl 1201.60078) Full Text: DOI arXiv EuDML
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi On heat kernel estimates and parabolic Harnack inequality for jump processes on metric measure spaces. (English) Zbl 1171.60373 Acta Math. Sin., Engl. Ser. 25, No. 7, 1067-1086 (2009). MSC: 60J75 60J35 31C25 31C05 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., Acta Math. Sin., Engl. Ser. 25, No. 7, 1067--1086 (2009; Zbl 1171.60373) Full Text: DOI
Barlow, Martin T.; Grigor’yan, Alexander; Kumagai, Takashi Heat kernel upper bounds for jump processes and the first exit time. (English) Zbl 1158.60039 J. Reine Angew. Math. 626, 135-157 (2009). Reviewer: Dian K. Palagachev (Bari) MSC: 60J99 60J75 PDFBibTeX XMLCite \textit{M. T. Barlow} et al., J. Reine Angew. Math. 626, 135--157 (2009; Zbl 1158.60039) Full Text: DOI
Chen, Zhen-Qing; Kim, Panki; Kumagai, Takashi Weighted Poincaré inequality and heat kernel estimates for finite range jump processes. (English) Zbl 1156.60069 Math. Ann. 342, No. 4, 833-883 (2008). Reviewer: Feng-Yu Wang (Swansea) MSC: 60J75 47G10 PDFBibTeX XMLCite \textit{Z.-Q. Chen} et al., Math. Ann. 342, No. 4, 833--883 (2008; Zbl 1156.60069) Full Text: DOI
Chen, Zhen-Qing; Kumagai, Takashi Heat kernel estimates for jump processes of mixed types on metric measure spaces. (English) Zbl 1131.60076 Probab. Theory Relat. Fields 140, No. 1-2, 277-317 (2008). MSC: 60J75 60J35 31C25 31C05 PDFBibTeX XMLCite \textit{Z.-Q. Chen} and \textit{T. Kumagai}, Probab. Theory Relat. Fields 140, No. 1--2, 277--317 (2008; Zbl 1131.60076) Full Text: DOI
Hu, Jiaxin; Kumagai, Takashi Nash-type inequalities and heat kernels for non-local Dirichlet forms. (English) Zbl 1119.60068 Kyushu J. Math. 60, No. 2, 245-265 (2006). Reviewer: Mohamed Hmissi (Tunis) MSC: 60J75 60J35 46E35 60J45 PDFBibTeX XMLCite \textit{J. Hu} and \textit{T. Kumagai}, Kyushu J. Math. 60, No. 2, 245--265 (2006; Zbl 1119.60068) Full Text: DOI
Kumagai, Takashi Function spaces and stochastic processes of fractals. (English) Zbl 1081.60059 Bandt, Christoph (ed.) et al., Fractal geometry and stochastics III. Proceedings of the 3rd conference, Friedrichroda, Germany, March 17–22, 2003. Basel: Birkhäuser (ISBN 3-7643-7070-X/hbk). Progress in Probability 57, 221-234 (2004). Reviewer: René L. Schilling (Marburg) MSC: 60J75 60J65 28A80 46E35 60J35 31C25 PDFBibTeX XMLCite \textit{T. Kumagai}, Prog. Probab. 57, 221--234 (2004; Zbl 1081.60059)
Chen, Zhen-Qing; Kumagai, Takashi Heat kernel estimates for stable-like processes on \(d\)-sets. (English) Zbl 1075.60556 Stochastic Processes Appl. 108, No. 1, 27-62 (2003). Reviewer: Jan Seidler (Praha) MSC: 60J35 60J75 PDFBibTeX XMLCite \textit{Z.-Q. Chen} and \textit{T. Kumagai}, Stochastic Processes Appl. 108, No. 1, 27--62 (2003; Zbl 1075.60556) Full Text: DOI
Kumagai, Takashi Some remarks for stable-like jump processes on fractals. (English) Zbl 1029.60067 Grabner, Peter (ed.) et al., Fractals in Graz 2001. Analysis, dynamics, geometry, stochastics. Proceedings of the conference, Graz, Austria, June 2001. Basel: Birkhäuser. Trends in Mathematics. 185-196 (2003). Reviewer: Yoichi Oshima (Kumamoto) MSC: 60J75 60J45 28A80 31C25 46E35 PDFBibTeX XMLCite \textit{T. Kumagai}, in: Fractals in Graz 2001. Analysis, dynamics, geometry, stochastics. Proceedings of the conference, Graz, Austria, June 2001. Basel: Birkhäuser. 185--196 (2003; Zbl 1029.60067)