A new setting for potential theory. I

Kai Lai Chung; K. Murali Rao

Annales de l'institut Fourier (1980)

  • Volume: 30, Issue: 3, page 167-198
  • ISSN: 0373-0956

Abstract

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We consider a transient Hunt process in which the potential density u satisfies the conditions: (a) for each x , u ( x , y ) - 1 is finite continuous in y ; (b) u ( x , y ) = + iff x = y . In earlier papers Chung established an equilibrium principle, and Rao obtained a Riesz of decomposition for excessive functions. We now begin a deeper study under these conditions, including the uniqueness of the decomposition and Hunt’s hypothesis (B).

How to cite

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Chung, Kai Lai, and Rao, K. Murali. "A new setting for potential theory. I." Annales de l'institut Fourier 30.3 (1980): 167-198. <http://eudml.org/doc/74458>.

@article{Chung1980,
abstract = {We consider a transient Hunt process in which the potential density $u$ satisfies the conditions: (a) for each $x$, $u(x,y)^\{-1\}$ is finite continuous in $y$; (b) $u(x,y)=+\infty $ iff $x=y$. In earlier papers Chung established an equilibrium principle, and Rao obtained a Riesz of decomposition for excessive functions. We now begin a deeper study under these conditions, including the uniqueness of the decomposition and Hunt’s hypothesis (B).},
author = {Chung, Kai Lai, Rao, K. Murali},
journal = {Annales de l'institut Fourier},
keywords = {new setting for potential theory; transient Hunt process; potential density; equilibrium principle; decomposition; uniqueness},
language = {eng},
number = {3},
pages = {167-198},
publisher = {Association des Annales de l'Institut Fourier},
title = {A new setting for potential theory. I},
url = {http://eudml.org/doc/74458},
volume = {30},
year = {1980},
}

TY - JOUR
AU - Chung, Kai Lai
AU - Rao, K. Murali
TI - A new setting for potential theory. I
JO - Annales de l'institut Fourier
PY - 1980
PB - Association des Annales de l'Institut Fourier
VL - 30
IS - 3
SP - 167
EP - 198
AB - We consider a transient Hunt process in which the potential density $u$ satisfies the conditions: (a) for each $x$, $u(x,y)^{-1}$ is finite continuous in $y$; (b) $u(x,y)=+\infty $ iff $x=y$. In earlier papers Chung established an equilibrium principle, and Rao obtained a Riesz of decomposition for excessive functions. We now begin a deeper study under these conditions, including the uniqueness of the decomposition and Hunt’s hypothesis (B).
LA - eng
KW - new setting for potential theory; transient Hunt process; potential density; equilibrium principle; decomposition; uniqueness
UR - http://eudml.org/doc/74458
ER -

References

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  1. [1] R.M. BLUMENTHAL and R.K. GETOOR, Markov Processes and Potential Theory, Academic Press, 1968. Zbl0169.49204MR41 #9348
  2. [2] K.L. CHUNG, Probabilistic approach in potential theory to the equilibrium problem, Ann. Inst. Fourier, 23, 3 (1973), 313-322. Zbl0258.31012MR52 #12098
  3. [3] G.A. HUNT, Markoff processes and potentials I, Illinois J. Math., 1 (1957), 43-93. Zbl0100.13804MR19,951g
  4. [4] P.A. MEYER, Probabilités et potentiel, Hermann, 1966. Zbl0138.10402MR34 #5118
  5. [5] P.A. MEYER, Processus de Markov : la frontière de Martin, Lecture Notes in Mathematics No. 77, Springer-Verlag, (1968). Zbl0174.49303MR39 #7669
  6. [6] P.A. MEYER, Deux petits résultats de théorie du potentiel, Séminaire de Probabilités V, Lecture Notes in Mathematics No. 191, Springer-Verlag (1971), 211-212. 
  7. [7] P.A. MEYER, Le Retournement du temps, d'après Chung et Walsh, Séminaire de Probabilités V, Lecture Notes in Mathematics No. 191, Springer-Verlag (1971), 213-236. 
  8. [8] G. MOKOBODZKI, Densité relative de deux potentiels comparables, Séminaire de Probabilités IV, Lecture Notes in Mathematics No. 124, Springer-Verlag (1970), 170-194. Zbl0218.31014MR45 #3747
  9. [9] K.M. RAO, Excessive functions as potentials of measures, J. London Math. Soc., 16 (1977), 165-171. Zbl0369.31007MR57 #10833

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