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Balayage of Semi-Dirichlet Forms

Published online by Cambridge University Press:  20 November 2018

Ze-Chun Hu  and
Wei Sun
Ze-Chun Hu
Affiliation:
Department of Mathematics, Nanjing University, Nanjing, 210093, China email: [email protected]
Wei Sun
Affiliation:
Department of Mathematics and Statistics, Concordia University, Montreal, H3G 1M8 email: [email protected]
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Abstract

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In this paper we study the balayage of semi-Dirichlet forms. We present new results on balayaged functions and balayaged measures of semi-Dirichlet forms. Some of the results are new even in the Dirichlet forms setting.

Keywords

31C2560J45balayagesemi-Dirichlet formpotential theory
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 64 , Issue 4 , 01 August 2012 , pp. 869 - 891
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Beznea, L. and Boboc, N., Potential theory and right processes. Mathematics and its Applications, 572, Kluwer Academic Publishers, Dordrecht, 2004.Google Scholar
[2] Bliedtner, J. and Hansen, W., Potential theory, an analytic and probabilistic approach to balayage. Universitext, Springer-Verlag, Berlin, 1986.Google Scholar
[3] Chen, Z.-Q., Fukushima, M., and Ying, J., Traces of symmetric Markov processes and their characterizations. Ann. Probab. 34(2006), no. 3, 1052–1102. http://dx.doi.org/10.1214/009117905000000657 Google Scholar
[4] Chen, Z.-Q., Entrance law, exit system and Levy system of time changed processes. Illinois J. Math. 50(2006), no. 1–4, 269–312.Google Scholar
[5] Doob, J. L., Classical potential theory and its probabilistic counterpart. Grundlehren der Mathematischen Wissenschaften, 262, Springer-Verlag, New York, 1984.Google Scholar
[6] Feyel, D., Sur la théorie fine du potentiel. Bull. Soc. Math. France 111(1983), no. 1, 41–57.Google Scholar
[7] Fitzsimmons, P. J., On the quasi-regularity of semi-Dirichlet forms. Potential Anal. 15(2001), no. 3, 151–185. http://dx.doi.org/10.1023/A:1011249920221 Google Scholar
[8] Fitzsimmons, P. J. and Getoor, R. K., Lévy systems and time changes. In: Séminaire de Probabilités XLII, Lecture Notes in Math., 1979, Springer, Berlin, 2009, pp. 229–259.Google Scholar
[9] Fukushima, M., He, P., and Ying, J., Time changes of symmetric diffusions and Feller measures. Ann. Probab. 32(2004), no. 4, 3138–3166. http://dx.doi.org/10.1214/009117904000000649 Google Scholar
[10] Fukushima, M., Oshima, Y., and Takeda, M., Dirichlet forms and symmetric Markov processes. de Gruyter Studies in Mathematics, 19, Walter de Gruyter, Berlin, 1994.Google Scholar
[11] Fukushima, M. and Uemura, T., Jump-type processes generated by lower bounded semi-Dirichlet forms. Ann. Probab., to appear. http://www.imstat.org/aop/future papers.htm Google Scholar
[12] Hu, Z.-C. and Z.-M.Ma, Beurling-Deny formula of semi-Dirichlet forms. C. R.Math. Acad. Sci. Paris 338(2004), no. 7, 521–526.Google Scholar
[13] Hu, Z.-C., Ma, Z.-M., and W. Sun, Extensions of Lévy-Khintchine formula and Beurling-Deny formula in semi-Dirichlet forms setting. J. Funct. Anal. 239(2006), no. 1, 179–213. http://dx.doi.org/10.1016/j.jfa.2005.12.015 Google Scholar
[14] Hu, Z.-C., Some remarks on representations of non-symmetric local Dirichlet forms. In: Potential Theory and Stochastics in Albac, Theta Ser. Adv. Math., 11, Theta, Bucharest, 2009, pp. 145–156.Google Scholar
[15] Hu, Z.-C., On representations of non-symmetric Dirichlet forms. Potential Anal. 32(2010), no. 2, 101–131. http://dx.doi.org/10.1007/s11118-009-9145-5 Google Scholar
[16] Kuwae, K., Maximum principles for subharmonic functions via local semi-Dirichlet forms. Canad. J. Math. 60(2008), no. 4, 822–874. http://dx.doi.org/10.4153/CJM-2008-036-8 Google Scholar
[17] Le Jan, Y., Balayage et formes de Dirichlet. Z.Warsch. Verw. Gebiete 37(1976/77), no. 4, 297–319.Google Scholar
[18] Le Jan, Y., Mesures associées à une forme de Dirichlet. Applications. Bull. Soc. Math. France 106(1978), no. 1, 61–112.Google Scholar
[19] Ma, Z. M., Overbeck, L., and Röckner, M., Markov processes associated with semi-Dirichlet forms. Osaka J. Math. 32(1995), no. 1, 97–119.Google Scholar
[20] Ma, Z. M. and Röckner, M., Introduction to the Theory of (Non-Symmetric) Dirichlet Forms. Springer-Verlag, Berlin-Heidelberg-New York, 1992.Google Scholar
[21] Ma, Z. M. and Röckner, M., Markov processes associated with positivity preserving coercive forms. Canad. J. Math. 47(1995), no. 4, 817–840. http://dx.doi.org/10.4153/CJM-1995-042-6 Google Scholar
[22] Ma, Z. M. and Sun, W., Some topics on Dirichlet forms. In: New trends in stochastic analysis and related topics: a volume in honour of Professor K. D. Elworthy. World Scientific Publishing Company, 2011.Google Scholar
[23] Overbeck, L., Röckner, M., and Schmuland, B., An analytic approach to Fleming-Viot processes with interactive selection. Ann. Probab. 23(1995), no. 1, 1–36. http://dx.doi.org/10.1214/aop/1176988374 Google Scholar
[24] Röckner, M. and Schmuland, B., Quasi-regular Dirichlet forms: examples and counterexamples. Canad. J. Math. 47(1995), no. 1, 165–200. http://dx.doi.org/10.4153/CJM-1995-009-3 Google Scholar
[25] Silverstein, M., Dirichlet spaces and random time change. Illinois J. Math. 17(1973), 1–72.Google Scholar
[26] Silverstein, M., The reflected Dirichlet space. Illinois J. Math. 18(1974), 310–355.Google Scholar
[27] Silverstein, M., Symmetric Markov processes. Lecture Notes in Math., 426, Springer-Verlag, Berlin-New York, 1974.Google Scholar