Hitting distributions domination and subordinate resolvents; an analytic approach

Nicu Boboc; Gheorghe Bucur

Open Mathematics (2006)

  • Volume: 4, Issue: 1, page 138-162
  • ISSN: 2391-5455

Abstract

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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

How to cite

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Nicu Boboc, and Gheorghe Bucur. "Hitting distributions domination and subordinate resolvents; an analytic approach." Open Mathematics 4.1 (2006): 138-162. <http://eudml.org/doc/268699>.

@article{NicuBoboc2006,
abstract = {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},
author = {Nicu Boboc, Gheorghe Bucur},
journal = {Open Mathematics},
keywords = {31D05; 60J45; 60J35},
language = {eng},
number = {1},
pages = {138-162},
title = {Hitting distributions domination and subordinate resolvents; an analytic approach},
url = {http://eudml.org/doc/268699},
volume = {4},
year = {2006},
}

TY - JOUR
AU - Nicu Boboc
AU - Gheorghe Bucur
TI - Hitting distributions domination and subordinate resolvents; an analytic approach
JO - Open Mathematics
PY - 2006
VL - 4
IS - 1
SP - 138
EP - 162
AB - 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
LA - eng
KW - 31D05; 60J45; 60J35
UR - http://eudml.org/doc/268699
ER -

References

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  1. [1] H. Ben Saad: Généralisation des noyaux V het applications, Lecture Notes in Math, Vol. 196, Springer Verlag, (1984), pp. 14-39. 
  2. [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. Zbl0864.31009
  3. [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. Zbl0860.31007
  4. [4] L. Beznea and N. Boboc: Potential Theory and Right Processes, Kluwer Acad. Publish., 2004. 
  5. [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. Zbl0846.31013
  6. [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. Zbl0866.31009
  7. [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. Zbl0537.60071
  8. [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. [9] P.A. Meyer: “Fonctionelles multiplicatives et additives de Markov”, Ann. Inst. Fourier (Grenoble), Vol. 12, (1962), pp. 125–230. Zbl0138.40802
  10. [10] G. Mokobodzki: Operateur de subordination des resolventes, 1983, unpublished manuscript. 
  11. [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 Zbl0178.20504

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