V: 06, 76-76, LNM 191 (1971)
CHUNG, Kai Lai
A simple proof of Doob's convergence theorem (
Potential theory)
Doob's theorem is a version of the main convergence theorem of potential theory: the limit of a decreasing sequence of excessive functions differs of its regularized version on a semi-polar set
Comment: It is also shown that a function $f$ satisfying $f\ge P_Kf$ for all compact sets $K$ differs from its regularized function on a semi-polar set
Keywords: Excessive functions,
Semi-polar setsNature: New exposition of known results
Retrieve article from Numdam
VI: 05, 90-97, LNM 258 (1972)
CHUNG, Kai Lai
On universal field equations (
General theory of processes)
There is a pun in the title, since ``field'' here is a $\sigma$-field and not a quantum field. The author proves useful results on the $\sigma$-fields ${\cal F}_{T-}$ and ${\cal F}_{T+}$ associated with an arbitrary random variable $T$ in the paper of Chung-Doob,
Amer. J. Math.,
87, 1965. As a corollary, he can prove easily that for a Hunt process, accessible = previsible
Keywords: FiltrationsNature: Original Retrieve article from Numdam
VIII: 03, 20-21, LNM 381 (1974)
CHUNG, Kai Lai
Note on last exit decomposition (
Markov processes)
This is a useful complement to the monograph of Chung
Lectures on Boundary Theory for Markov Chains, Annals of Math. Studies 65, Princeton 1970
Keywords: Markov chainsNature: Original Retrieve article from Numdam
XI: 03, 27-33, LNM 581 (1977)
CHUNG, Kai Lai
Pedagogic notes on the barrier theorem (
Potential theory)
Let $D$ a bounded open set in $
R^n$, and let $z$ be a boundary point. Then a barrier at $z$ is a superharmonic function in $D$, strictly positive and with a limit equal to $0$ at $z$. The barrier theorem asserts that if there is a barrier at $z$, then $z$ is regular. An elegant proof of this is given using Brownian motion. Then it is shown that the expectation of $S$, the hitting time of $D^c$, is bounded, upper semi-continuous in $R^n$ and continuous in $D$, and is a barrier at every regular point
Comment: An error is corrected in
1247Keywords: Classical potential theory,
Barrier,
Regular pointsNature: New proof of known results Retrieve article from Numdam
XII: 47, 739-739, LNM 649 (1978)
CHUNG, Kai Lai
Correction to "Pedagogic Notes on the Barrier Theorem" (
Potential theory)
Corrects an error in
1103Keywords: Classical potential theory,
Barrier,
Regular pointsNature: Correction Retrieve article from Numdam
XIV: 39, 347-356, LNM 784 (1980)
CHUNG, Kai Lai
On stopped Feynman-Kac functionals (
Markov processes,
Diffusion theory)
Let $(X_t)$ be a strong Markov process with continuous paths on the line, and let $\tau_b$ be the hitting time of the point $b$. It is assumed that $\tau_b$ is $P_a$-a.s. finite for all $a,b$. The purpose of the paper is to study the quantities $u(a,b)=E_a[\,\exp(\int_0^{\tau_b} q(X_s)\,ds)\,]$ where $q$ is bounded. Then (among other results) if $u(a,b)<\infty$ for all $a<b$, we have $u(a,b)\,u(b,a)\le 1$ for all $a,b$
Keywords: Hitting probabilitiesNature: Original Retrieve article from Numdam
XIX: 33, 496-503, LNM 1123 (1985)
CHUNG, Kai Lai
The gauge and conditional gauge theorem Retrieve article from Numdam
XX: 28, 423-425, LNM 1204 (1986)
CHUNG, Kai Lai
Remark on the conditional gauge theorem Retrieve article from Numdam
