B. Baeumer and M. M. Meerschaert, Stochastic solutions for fractional Cauchy problems, Fract. Calc. Appl. Anal. 4 (2001), no. 4, 481–500. Google Scholar
M. T. Barlow and J. Černý, Convergence to fractional kinetics for random walks associated with unbounded conductances, Probab. Theory Related Fields 149 (2011), no. 3–4, 639–673. Web of ScienceCrossrefGoogle Scholar
Z.-Q. Chen and M. Fukushima, Symmetric Markov Processes, Time Change, and Boundary Theory, London Math. Soc. Monogr. Ser. 35, Princeton University Press, Princeton, 2012. Google Scholar
Z.-Q. Chen, T. Kumagai and J. Wang, Stability of heat kernel estimates for symmetric jump processes on metric measure spaces, preprint (2016), https://arxiv.org/abs/1604.04035.
A. Grigor’yan and T. Kumagai, On the dichotomy in the heat kernel two sided estimates, Analysis on Graphs and Its Applications, Proc. Sympos. Pure Math. 77, American Mathematical Society, Providence (2008), 199–210. Google Scholar
B. M. Hambly and T. Kumagai, Transition density estimates for diffusion processes on post critically finite self-similar fractals, Proc. Lond. Math. Soc. (3) 78 (1999), no. 2, 431–458. CrossrefGoogle Scholar
M. M. Meerschaert and A. Sikorskii, Stochastic Models for Fractional Calculus, De Gruyter Stud. Math. 43, Walter de Gruyter, Berlin, 2012. Google Scholar
J. Nakagawa, Personal communications.
J. Nakagawa, K. Sakamoto and M. Yamamoto, Overview to mathematical analysis for fractional diffusion equations—new mathematical aspects motivated by industrial collaboration, J. Math. Ind. 2A (2010), 99–108. Google Scholar
R. L. Schilling, R. Song and Z. Vondraček, Bernstein Functions. Theory and Applications, 2nd ed., De Gruyter Stud. Math. 37, Walter de Gruyter & Co., Berlin, 2010. Google Scholar
A. Telcs, The Art of Random Walks, Lecture Notes in Math. 1885, Springer, Berlin, 2006. Google Scholar
About the article
Published Online: 2018-02-16
Published in Print: 2018-09-01
Funding Source: National Research Foundation of Korea
Award identifier / Grant number: 2016R1E1A1A01941893
Funding Source: National Natural Science Foundation of China
Award identifier / Grant number: 11522106
Funding Source: Japan Society for the Promotion of Science
Award identifier / Grant number: 26
Funding Source: Natural Science Foundation of Fujian Province
Award identifier / Grant number: 2015J01003
The research of Panki Kim is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1E1A1A01941893). The research of Takashi Kumagai is supported by the Grant-in-Aid for Scientific Research (A) 25247007 and 17H01093, Japan. The research of Jian Wang is supported by National Natural Science Foundation of China (No. 11522106), the JSPS postdoctoral fellowship (2604021), Fok Ying Tung Education Foundation (No. 151002), National Science Foundation of Fujian Province (No. 2015J01003), the Program for Probability and Statistics: Theory and Application (No. IRTL1704), and Fujian Provincial Key Laboratory of Mathematical Analysis and its Applications (FJKLMAA).