K. L. Chung and J. B. Walsh :
“To reverse a Markov process ,”
Acta Math.
123 : 1
(1969 ),
pp. 225–251 .
MR
0258114
Zbl
0187.41302
article

People
BibTeX
@article {key0258114m,
AUTHOR = {Chung, K. L. and Walsh, John B.},
TITLE = {To reverse a {M}arkov process},
JOURNAL = {Acta Math.},
FJOURNAL = {Acta Mathematica},
VOLUME = {123},
NUMBER = {1},
YEAR = {1969},
PAGES = {225--251},
DOI = {10.1007/BF02392389},
NOTE = {MR:0258114. Zbl:0187.41302.},
ISSN = {0001-5962},
}
K. L. Chung :
“On the fundamental hypotheses of Hunt processes ,”
pp. 43–52
in
Convegno di calcolo delle probabilità
(INDAM, Rome, March–April, 1971 ).
Edited by F. Severi .
Symposia Mathematica IX .
Academic Press (London ),
1972 .
MR
0359019
Zbl
0242.60031
incollection

People
BibTeX
@incollection {key0359019m,
AUTHOR = {Chung, Kai Lai},
TITLE = {On the fundamental hypotheses of {H}unt
processes},
BOOKTITLE = {Convegno di calcolo delle probabilit\`a},
EDITOR = {Severi, Francesco},
SERIES = {Symposia {M}athematica},
NUMBER = {IX},
PUBLISHER = {Academic Press},
ADDRESS = {London},
YEAR = {1972},
PAGES = {43--52},
NOTE = {(INDAM, Rome, March--April, 1971). MR:0359019.
Zbl:0242.60031.},
}
K. L. Chung :
“Probabilistic approach in potential theory to the equilibrium problem ,”
Ann. Inst. Fourier (Grenoble)
23 : 3
(1973 ),
pp. 313–322 .
MR
0391277
Zbl
0258.31012
article

Abstract
BibTeX
@article {key0391277m,
AUTHOR = {Chung, Kai Lai},
TITLE = {Probabilistic approach in potential
theory to the equilibrium problem},
JOURNAL = {Ann. Inst. Fourier (Grenoble)},
FJOURNAL = {Universit\'e de Grenoble. Annales de
l'Institut Fourier},
VOLUME = {23},
NUMBER = {3},
YEAR = {1973},
PAGES = {313--322},
URL = {http://www.numdam.org/item?id=AIF_1973__23_3_313_0},
NOTE = {MR:0391277. Zbl:0258.31012.},
ISSN = {0373-0956},
}
K. L. Chung :
“Remarks on equilibrium potential and energy ,”
pp. xiv, 131–138
in
Collection of articles dedicated to Marcel Brelot on the occasion of his 70th birthday ,
published as Ann. Inst. Fourier (Grenoble)
25 : 3–4
(1975 ).
MR
0405601
Zbl
0338.31001
incollection

Abstract
People
BibTeX
@article {key0405601m,
AUTHOR = {Chung, Kai Lai},
TITLE = {Remarks on equilibrium potential and
energy},
JOURNAL = {Ann. Inst. Fourier (Grenoble)},
FJOURNAL = {Universit\'e de Grenoble. Annales de
l'Institut Fourier},
VOLUME = {25},
NUMBER = {3--4},
YEAR = {1975},
PAGES = {xiv, 131--138},
URL = {http://www.numdam.org/item?id=AIF_1975__25_3-4_131_0},
NOTE = {\textit{Collection of articles dedicated
to {M}arcel {B}relot on the occasion
of his 70th birthday}. MR:0405601. Zbl:0338.31001.},
ISSN = {0373-0956},
}
K. L. Chung :
“Maxima in Brownian excursions ,”
Bull. Amer. Math. Soc.
81 : 4
(July 1975 ),
pp. 742–745 .
MR
0373035
Zbl
0325.60077
article

BibTeX
@article {key0373035m,
AUTHOR = {Chung, Kai Lai},
TITLE = {Maxima in {B}rownian excursions},
JOURNAL = {Bull. Amer. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {81},
NUMBER = {4},
MONTH = {July},
YEAR = {1975},
PAGES = {742--745},
DOI = {10.1090/S0002-9904-1975-13852-3},
NOTE = {MR:0373035. Zbl:0325.60077.},
ISSN = {0002-9904},
}
K. L. Chung :
“Excursions in Brownian motion ,”
Ark. Mat.
14 : 1–2
(1976 ),
pp. 155–177 .
Dedicated to the Memory of Paul Lévy.
MR
0467948
Zbl
0356.60033
article

People
BibTeX
@article {key0467948m,
AUTHOR = {Chung, Kai Lai},
TITLE = {Excursions in {B}rownian motion},
JOURNAL = {Ark. Mat.},
FJOURNAL = {Arkiv f\"or Matematik},
VOLUME = {14},
NUMBER = {1--2},
YEAR = {1976},
PAGES = {155--177},
DOI = {10.1007/BF02385832},
NOTE = {Dedicated to the Memory of Paul L\'evy.
MR:0467948. Zbl:0356.60033.},
ISSN = {0004-2080},
}
K. L. Chung and J. Glover :
“Left continuous moderate Markov processes ,”
Z. Wahrsch. Verw. Gebiete
49 : 3
(1979 ),
pp. 237–248 .
MR
547825
Zbl
0413.60063
article

Abstract
People
BibTeX
@article {key547825m,
AUTHOR = {Chung, Kai Lai and Glover, Joseph},
TITLE = {Left continuous moderate {M}arkov processes},
JOURNAL = {Z. Wahrsch. Verw. Gebiete},
FJOURNAL = {Zeitschrift f\"ur Wahrscheinlichkeitstheorie
und Verwandte Gebiete},
VOLUME = {49},
NUMBER = {3},
YEAR = {1979},
PAGES = {237--248},
DOI = {10.1007/BF00535496},
NOTE = {MR:547825. Zbl:0413.60063.},
ISSN = {0044-3719},
}
K. L. Chung and M. Rao :
“Equilibrium and energy ,”
Probab. Math. Statist.
1 : 2
(1980 ),
pp. 99–108 .
MR
626304
Zbl
0502.60060
article

Abstract
People
BibTeX

In this paper it is shown that the equilibrium measure \( \nu \) for a compact \( K \) in potential theory can be related with a unique invariant measure \( \pi \) for a discrete time Markov process by the formula
\[ \pi(dy) = \phi(y)\,\nu(dy) .\]
The chain has the transition function \( L(x,A) \) , where \( L \) is the last-exit kernel in [Chung 1973]. For a general non-symmetric potential density \( u \) the modified energy
\[ I(\lambda) = \iint \lambda(dx)\,u(x,y)\,\phi(y)^{-1}(dy) \]
and the Gauss quadratic
\[ G(\lambda) = I(\lambda) - 2\lambda(K) \]
are introduced. Then \( G \) is minimized by \( \pi \) among all signed measures \( \lambda \) on \( K \) of finite modified energy, provided \( I \) is positive. This includes the classical symmetric case of Newtonian and M. Riesz potentials as a special case. The modification corresponds to a time change for the underlying Markov process. The positivity of \( I \) is established for a class of signed measures associated with continuous additive functionals in the sense of Revuz.

@article {key626304m,
AUTHOR = {Chung, Kai Lai and Rao, Murali},
TITLE = {Equilibrium and energy},
JOURNAL = {Probab. Math. Statist.},
FJOURNAL = {Probability and Mathematical Statistics},
VOLUME = {1},
NUMBER = {2},
YEAR = {1980},
PAGES = {99--108},
URL = {http://www.math.uni.wroc.pl/~pms/files/1.2/Abstract/1.2.1.abs.pdf},
NOTE = {MR:626304. Zbl:0502.60060.},
ISSN = {0208-4147},
}
K. L. Chung and K. M. Rao :
“A new setting for potential theory, I ,”
Ann. Inst. Fourier (Grenoble)
30 : 3
(1980 ),
pp. 167–198 .
MR
597022
Zbl
0424.31004
article

Abstract
People
BibTeX

In Hunt’s theory of Markov processes certain duality assumptions are made to generalize well known classical potential theoretic results such as F. Riesz representation theorem, uniqueness, existence of equilibrium potential, etc. A standard treatment developed by several subsequent authors can be found in [Blumenthal and Getoor 1968]. In a different direction, it was shown in [Chung 1973] under simple analytic conditions that the equilibrium measure is inherently linked to the last exit distribution of the process. It thus appears feasible that this last result, namely on “equilibrium principle” may be made the starting point to which other major results are related.

In this paper we exploit the line of thought in [Chung 1973] to derive some of these major results under the same set of conditions as in [Chung 1973]. It turns out that these sets of conditions automatically imply the existence of a dual. However, this will not be proved here.

@article {key597022m,
AUTHOR = {Chung, K. L. and Rao, K. Murali},
TITLE = {A new setting for potential theory,
{I}},
JOURNAL = {Ann. Inst. Fourier (Grenoble)},
FJOURNAL = {Universit\'e de Grenoble. Annales de
l'Institut Fourier},
VOLUME = {30},
NUMBER = {3},
YEAR = {1980},
PAGES = {167--198},
URL = {http://www.numdam.org/item?id=AIF_1980__30_3_167_0},
NOTE = {MR:597022. Zbl:0424.31004.},
ISSN = {0373-0956},
CODEN = {AIFUA7},
}
K. L. Chung, M. Liao, and K. M. Rao :
“Duality under a new setting ,”
pp. 23–38
in
Seminar on stochastic processes, 1983
(University of Florida, Gainesville, FL, 1983 ).
Edited by E. Çinlar, K. L. Chung, and R. K. Getoor .
Progress in Probability and Statistics 7 .
Birkhäuser (Boston, MA ),
1984 .
MR
902410
Zbl
0558.60056
incollection

People
BibTeX
@incollection {key902410m,
AUTHOR = {Chung, K. L. and Liao, Ming and Rao,
K. M.},
TITLE = {Duality under a new setting},
BOOKTITLE = {Seminar on stochastic processes, 1983},
EDITOR = {Erhan \c{C}inlar and K. L. Chung and
R. K. Getoor},
SERIES = {Progress in Probability and Statistics},
NUMBER = {7},
PUBLISHER = {Birkh\"auser},
ADDRESS = {Boston, MA},
YEAR = {1984},
PAGES = {23--38},
NOTE = {(University of Florida, Gainesville,
FL, 1983). MR:902410. Zbl:0558.60056.},
ISBN = {081763293X, 9780817632939},
}