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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 sets

Nature: New exposition of known results

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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: Filtrations

Nature: Original

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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 chains

Nature: Original

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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 1247

Keywords: Classical potential theory, Barrier, Regular points

Nature: New proof of known results

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XII: 47, 739-739, LNM 649 (1978)

**CHUNG, Kai Lai**

Correction to "Pedagogic Notes on the Barrier Theorem" (Potential theory)

Corrects an error in 1103

Keywords: Classical potential theory, Barrier, Regular points

Nature: Correction

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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 probabilities

Nature: Original

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XIX: 33, 496-503, LNM 1123 (1985)

**CHUNG, Kai Lai**

The gauge and conditional gauge theorem

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XX: 28, 423-425, LNM 1204 (1986)

**CHUNG, Kai Lai**

Remark on the conditional gauge theorem

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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 sets

Nature: New exposition of known results

Retrieve article from Numdam

VI: 05, 90-97, LNM 258 (1972)

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,

Keywords: Filtrations

Nature: Original

Retrieve article from Numdam

VIII: 03, 20-21, LNM 381 (1974)

Note on last exit decomposition (Markov processes)

This is a useful complement to the monograph of Chung

Keywords: Markov chains

Nature: Original

Retrieve article from Numdam

XI: 03, 27-33, LNM 581 (1977)

Pedagogic notes on the barrier theorem (Potential theory)

Let $D$ a bounded open set in $

Comment: An error is corrected in 1247

Keywords: Classical potential theory, Barrier, Regular points

Nature: New proof of known results

Retrieve article from Numdam

XII: 47, 739-739, LNM 649 (1978)

Correction to "Pedagogic Notes on the Barrier Theorem" (Potential theory)

Corrects an error in 1103

Keywords: Classical potential theory, Barrier, Regular points

Nature: Correction

Retrieve article from Numdam

XIV: 39, 347-356, LNM 784 (1980)

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 probabilities

Nature: Original

Retrieve article from Numdam

XIX: 33, 496-503, LNM 1123 (1985)

The gauge and conditional gauge theorem

Retrieve article from Numdam

XX: 28, 423-425, LNM 1204 (1986)

Remark on the conditional gauge theorem

Retrieve article from Numdam