Mean value inequalities for jump processes

Zhen Qing Chen; Takashi Kumagai; Jian Wang

doi:10.1007/978-3-319-74929-7_28

Mean value inequalities for jump processes

Zhen Qing Chen, Takashi Kumagai^*, Jian Wang

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

Parabolic Harnack inequalities are one of the most important inequalities in analysis and PDEs, partly because they imply Hölder regularity of the solutions of heat equations. Mean value inequalities play an important role in deriving parabolic Harnack inequalities. In this paper, we first survey the recent results obtained in Chen et al. (Stability of heat kernel estimates for symmetric non-local Dirichlet forms, 2016, [15]; Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms, 2016, [16]) on the study of stability of heat kernel estimates and parabolic Harnack inequalities for symmetric jump processes on general metric measure spaces. We then establish the L^p -mean value inequalities for all p∈ (0, 2] for these processes.

Original language	English
Title of host publication	Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016
Editors	Gerald Trutnau, Andreas Eberle, Walter Hoh, Moritz Kassmann, Martin Grothaus, Wilhelm Stannat
Publisher	Springer New York LLC
Pages	421-437
Number of pages	17
ISBN (Print)	9783319749280
DOIs	https://doi.org/10.1007/978-3-319-74929-7_28
Publication status	Published - 2018
Externally published	Yes
Event	International conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016 - Bielefeld, Germany Duration: 2016 Oct 10 → 2016 Oct 14

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	229
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Other

Other	International conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016
Country/Territory	Germany
City	Bielefeld
Period	16/10/10 → 16/10/14

Keywords

Harnack inequality
Heat kernel estimate
Mean value inequality
Stability
Symmetric jump process

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/978-3-319-74929-7_28

Cite this

Chen, Z. Q., Kumagai, T., & Wang, J. (2018). Mean value inequalities for jump processes. In G. Trutnau, A. Eberle, W. Hoh, M. Kassmann, M. Grothaus, & W. Stannat (Eds.), Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016 (pp. 421-437). (Springer Proceedings in Mathematics and Statistics; Vol. 229). Springer New York LLC. https://doi.org/10.1007/978-3-319-74929-7_28

Mean value inequalities for jump processes. / Chen, Zhen Qing; Kumagai, Takashi; Wang, Jian.

Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016. ed. / Gerald Trutnau; Andreas Eberle; Walter Hoh; Moritz Kassmann; Martin Grothaus; Wilhelm Stannat. Springer New York LLC, 2018. p. 421-437 (Springer Proceedings in Mathematics and Statistics; Vol. 229).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Chen, ZQ, Kumagai, T & Wang, J 2018, Mean value inequalities for jump processes. in G Trutnau, A Eberle, W Hoh, M Kassmann, M Grothaus & W Stannat (eds), Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016. Springer Proceedings in Mathematics and Statistics, vol. 229, Springer New York LLC, pp. 421-437, International conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016, Bielefeld, Germany, 16/10/10. https://doi.org/10.1007/978-3-319-74929-7_28

Chen ZQ, Kumagai T, Wang J. Mean value inequalities for jump processes. In Trutnau G, Eberle A, Hoh W, Kassmann M, Grothaus M, Stannat W, editors, Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016. Springer New York LLC. 2018. p. 421-437. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-319-74929-7_28

Chen, Zhen Qing ; Kumagai, Takashi ; Wang, Jian. / Mean value inequalities for jump processes. Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016. editor / Gerald Trutnau ; Andreas Eberle ; Walter Hoh ; Moritz Kassmann ; Martin Grothaus ; Wilhelm Stannat. Springer New York LLC, 2018. pp. 421-437 (Springer Proceedings in Mathematics and Statistics).

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author = "Chen, {Zhen Qing} and Takashi Kumagai and Jian Wang",

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AB - Parabolic Harnack inequalities are one of the most important inequalities in analysis and PDEs, partly because they imply Hölder regularity of the solutions of heat equations. Mean value inequalities play an important role in deriving parabolic Harnack inequalities. In this paper, we first survey the recent results obtained in Chen et al. (Stability of heat kernel estimates for symmetric non-local Dirichlet forms, 2016, [15]; Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms, 2016, [16]) on the study of stability of heat kernel estimates and parabolic Harnack inequalities for symmetric jump processes on general metric measure spaces. We then establish the Lp -mean value inequalities for all p∈ (0, 2] for these processes.

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Mean value inequalities for jump processes

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