We give an analytic version of the well known Shih's theorem concerning the Markov processes whose hitting distributions are dominated by those of a given process. The treatment is purely analytic, completely different from Shih's arguments and improves essentially his result (in the case when the given processes are transient
@article{bwmeta1.element.doi-10_1007_s11533-005-0009-y, author = {Nicu Boboc and Gheorghe Bucur}, title = {Hitting distributions domination and subordinate resolvents; an analytic approach}, journal = {Open Mathematics}, volume = {4}, year = {2006}, pages = {138-162}, zbl = {1103.31008}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1007_s11533-005-0009-y} }
Nicu Boboc; Gheorghe Bucur. Hitting distributions domination and subordinate resolvents; an analytic approach. Open Mathematics, Tome 4 (2006) pp. 138-162. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1007_s11533-005-0009-y/
[1] H. Ben Saad: Généralisation des noyaux V het applications, Lecture Notes in Math, Vol. 196, Springer Verlag, (1984), pp. 14-39.
[2] L. Beznea and N. Boboc: “Excessive functions and excessive measures: Hunt's theorem on balayages, quasi-continuity”, In: Classical and Modern Potential Theory and Appl., NATO ASI Series C, Vol. 430, Kluwer Acad. Publish., 1994, pp. 71–92. | Zbl 0864.31009
[3] L. Beznea and N. Boboc: “Kuran's regularity criterion and localization in excessive structures”, Bull. London Math. Soc., Vol. 28, (1996), pp. 273–282. | Zbl 0860.31007
[4] L. Beznea and N. Boboc: Potential Theory and Right Processes, Kluwer Acad. Publish., 2004.
[5] N. Boboc and Gh. Bucur: “Excessive and supermedian functions with respect to subordinated resolvent of kernels”, Rev. Roum. Math. Pures et Appl., Vol. 39, (1994), pp. 875–878. | Zbl 0846.31013
[6] N. Boboc and Gh. Bucur: “Dilation operators in excessive structures; existence and uniqueness”, In: Potential Theory ICPT 94, Walter de Gruyter& Co, 1996, pp. 311–339. | Zbl 0866.31009
[7] J. Franchi and Y. Le Jan: “Sur les trajectoires intrinsèques des processus de Markov et le théorèm de Shih”, Ann. Inst. H. Poincaré Probab. Statist., Vol. 20, (1984), pp. 103–126. | Zbl 0537.60071
[8] P.A. Meyer: “Semi-groups en dualité”, In: Sém. de Th: du Potentiel (Brelot-Choquet-Deny) 5eannée: 1960/61, Vol. 10, Secrétariat math. Paris, 1961, p. 1–14.
[9] P.A. Meyer: “Fonctionelles multiplicatives et additives de Markov”, Ann. Inst. Fourier (Grenoble), Vol. 12, (1962), pp. 125–230. | Zbl 0138.40802
[10] G. Mokobodzki: Operateur de subordination des resolventes, 1983, unpublished manuscript.
[11] C.T. Shih: “Markov processus where hitting distributions are dominated by those of a given process”, Trans. Amer. Math. Soc., Vol. 129, (1967), pp. 157–179. http://dx.doi.org/10.2307/1994370 | Zbl 0178.20504