IX: 25, 466-470, LNM 465 (1975)
MEYER, Paul-André;
YAN, Jia-An
Génération d'une famille de tribus par un processus croissant (
General theory of processes)
The previsible and optional $\sigma$-fields of a filtration $({\cal F}_t)$ on $\Omega$ are studied without the usual hypotheses: no measure is involved, and the filtration is not right continuous. It is proved that if the $\sigma$-fields ${\cal F}_{t-}$ are separable, then so is the previsible $\sigma$-field, and the filtration is the natural one for a continuous strictly increasing process. A similar result is proved for the optional $\sigma$-field assuming $\Omega$ is a Blackwell space, and then every measurable adapted process is optional
Comment: Making the filtration right continuous generally destroys the separability of the optional $\sigma$-field
Keywords: Previsible processes,
Optional processesNature: Original
Retrieve article from Numdam
X: 20, 422-431, LNM 511 (1976)
YAN, Jia-An;
YOEURP, Chantha
Représentation des martingales comme intégrales stochastiques des processus optionnels (
Martingale theory,
Stochastic calculus)
An attempt to build a theory similar to the previsible representation property with respect to a basic local martingale, but using the optional stochastic integral instead of the standard one
Comment: Apparently this ``optional representation property'' has not been used since
Keywords: Optional stochastic integralsNature: Original Retrieve article from Numdam
XIV: 17, 148-151, LNM 784 (1980)
YAN, Jia-An
Remarques sur l'intégrale stochastique de processus non bornés (
Stochastic calculus)
It is shown how to develop the integration theory of unbounded previsible processes (due to Jacod
1126), starting from the elementary definition considered ``awkward'' in
1415Comment: Another approach to those integrals is due to L. Schwartz, in his article
1530 on formal semimartingales
Keywords: Stochastic integralsNature: Original Retrieve article from Numdam
XIV: 25, 220-222, LNM 784 (1980)
YAN, Jia-An
Caractérisation d'ensembles convexes de $L^1$ ou $H^1$ (
Stochastic calculus,
Functional analysis)
This is a new and simpler approach to the crucial functional analytic lemma in
1354 (the proof that semimartingales are the stochastic integrators in $L^0$). That is, given a convex set $K\subset L^1$ containing $0$, find a condition for the existence of $Z>0$ in $L^\infty$ such that $\sup_{X\in K}E[ZX]<\infty$. A similar result is discussed for $H^1$ instead of $L^1$
Comment: This lemma, instead of the original one, has proved very useful in mathematical finance
Keywords: Semimartingales,
Stochastic integrals,
Convex functionsNature: Original Retrieve article from Numdam
XIV: 26, 223-226, LNM 784 (1980)
YAN, Jia-An
Remarques sur certaines classes de semimartingales et sur les intégrales stochastiques optionnelles (
Stochastic calculus)
A class of semimartingales containing the special ones is introduced, which can be intrinsically decomposed into a continuous and a purely discontinuous part. These semimartingales have ``not too large totally inaccessible jumps''. In the second part of the paper, a non-compensated optional stochastic integral is defined, improving the results of Yor
1335Keywords: Semimartingales,
Optional stochastic integralsNature: Original Retrieve article from Numdam
XIV: 33, 305-315, LNM 784 (1980)
YAN, Jia-An
Sur une équation différentielle stochastique générale (
Stochastic calculus)
The differential equation considered is of the form $X_t= \Phi(X)_t+\int_0^tF(X)_s\,dM_s$, where $M$ is a semimartingale, $\Phi$ maps adapted cadlag processes into themselves, and $F$ maps adapted cadlag process into previsible processes---not locally bounded, this is the main technical point. Some kind of Lipschitz condition being assumed, existence, uniqueness and stability are proved
Keywords: Stochastic differential equationsNature: Original Retrieve article from Numdam
XVI: 29, 338-347, LNM 920 (1982)
YAN, Jia-An
À propos de l'intégrabilité uniforme des martingales exponentielles (
Martingale theory)
Sufficient conditions are given for the uniform integrability of the exponential ${\cal E}(M)$, where $M$ is a local martingale with jumps $\ge-1$, refining older results of Lépingle and Mémin, and of the author. They involve the Lévy measure of the martingale
Comment: In the lemma p.339 delete the assumption $0<\beta$
Keywords: Exponential martingalesNature: Original Retrieve article from Numdam
XVII: 07, 78-80, LNM 986 (1983)
YAN, Jia-An
Une remarque sur les solutions faibles des équations différentielles stochastiques unidimensionnelles Retrieve article from Numdam
XVII: 12, 121-122, LNM 986 (1983)
YAN, Jia-An
Sur un théorème de Kazamaki-Sekiguchi Retrieve article from Numdam
XVII: 18, 179-184, LNM 986 (1983)
HE, Sheng-Wu;
YAN, Jia-An;
ZHENG, Wei-An
Sur la convergence des semimartingales continues dans ${\bf R}^n$ et des martingales dans une variété (
Stochastic calculus,
Stochastic differential geometry)
Say that a continuous semimartingale $X$ with canonical decomposition $X_0+M+A$ converges perfectly on an event $E$ if both $M_t$ and $\int_0^t|dA_s|$ have an a.s. limit on $E$ when $t\rightarrow \infty $. It is established that if $A_t$ has the form $\int_0^tH_sd[M,M]_s$, $X$ converges perfectly on the event $\{\sup_t|X_t|+\lim\sup_tH_t <\infty \}$. A similar (but less simple) statement is shown for multidimensional $X$; and an application is given to martingales in manifolds: every point of a manifold $V$ (with a connection) has a neighbourhood $U$ such that, given any $V$-valued martingale $X$, almost all paths of $X$ that eventually remain in $U$ are convergent
Comment: The latter statement (martingale convergence) is very useful; more recent proofs use convex functions instead of perfect convergence. The next talk
1719 is a small remark on perfect convergence
Keywords: Semimartingales,
Martingales in manifoldsNature: Original Retrieve article from Numdam
XVII: 45, 512-512, LNM 986 (1983)
YAN, Jia-An
Correction au volume XVI Retrieve article from Numdam
XX: 22, 349-351, LNM 1204 (1986)
YAN, Jia-An
A comparison theorem for semimartingales and its applications Retrieve article from Numdam
XXI: 02, 8-26, LNM 1247 (1987)
MEYER, Paul-André;
YAN, Jia-An
À propos des distributions sur l'espace de Wiener Retrieve article from Numdam
XXI: 03, 27-33, LNM 1247 (1987)
YAN, Jia-An
Développement des distributions suivant les chaos de Wiener et applications à l'analyse stochastique Retrieve article from Numdam
XXII: 07, 89-91, LNM 1321 (1988)
YAN, Jia-An
A perturbation theorem for semigroups of linear operators Retrieve article from Numdam
XXII: 08, 92-100, LNM 1321 (1988)
YAN, Jia-An
A formula for densities of transition functions Retrieve article from Numdam
XXIII: 31, 382-392, LNM 1372 (1989)
MEYER, Paul-André;
YAN, Jia-An
Distributions sur l'espace de Wiener (suite), d'après Kubo et Yokoi Retrieve article from Numdam
XXIII: 32, 393-394, LNM 1372 (1989)
YAN, Jia-An
Sur la transformée de Fourier de H. H. Kuo Retrieve article from Numdam
XXIII: 33, 395-404, LNM 1372 (1989)
YAN, Jia-An
Generalizations of Gross' and Minlos' theorems Retrieve article from Numdam
XXV: 08, 61-78, LNM 1485 (1991)
MEYER, Paul-André;
YAN, Jia-An
Les ``fonctions caractéristiques'' des distributions sur l'espace de Wiener Retrieve article from Numdam
XXV: 09, 79-94, LNM 1485 (1991)
YAN, Jia-An
Notes on the Wiener semigroup and renormalization Retrieve article from Numdam
XXV: 10, 95-107, LNM 1485 (1991)
YAN, Jia-An
Some remarks on the theory of stochastic integration Retrieve article from Numdam
XXV: 36, 427-427, LNM 1485 (1991)
YAN, Jia-An
Correction au Séminaire XXIII Retrieve article from Numdam
XXX: 08, 104-107, LNM 1626 (1996)
YAN, Jia-An
An asymptotic evaluation of heat kernel for short time Retrieve article from Numdam
XXXII: 06, 56-66, LNM 1686 (1998)
STRICKER, Christophe;
YAN, Jia-An
Some remarks on the optional decomposition theorem Retrieve article from Numdam
