Browse by: Author name - Classification - Keywords - Nature

25 matches found
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 processes
Nature: Original
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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 integrals
Nature: Original
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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 1415
Comment: Another approach to those integrals is due to L. Schwartz, in his article 1530 on formal semimartingales
Keywords: Stochastic integrals
Nature: Original
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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 functions
Nature: Original
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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 1335
Keywords: Semimartingales, Optional stochastic integrals
Nature: Original
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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 equations
Nature: Original
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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 martingales
Nature: Original
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XVII: 07, 78-80, LNM 986 (1983)
YAN, Jia-An
Une remarque sur les solutions faibles des équations différentielles stochastiques unidimensionnelles
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XVII: 12, 121-122, LNM 986 (1983)
YAN, Jia-An
Sur un théorème de Kazamaki-Sekiguchi
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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 manifolds
Nature: Original
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XVII: 45, 512-512, LNM 986 (1983)
YAN, Jia-An
Correction au volume XVI
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XX: 22, 349-351, LNM 1204 (1986)
YAN, Jia-An
A comparison theorem for semimartingales and its applications
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XXI: 02, 8-26, LNM 1247 (1987)
MEYER, Paul-André; YAN, Jia-An
À propos des distributions sur l'espace de Wiener
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XXI: 03, 27-33, LNM 1247 (1987)
YAN, Jia-An
Développement des distributions suivant les chaos de Wiener et applications à l'analyse stochastique
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XXII: 07, 89-91, LNM 1321 (1988)
YAN, Jia-An
A perturbation theorem for semigroups of linear operators
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XXII: 08, 92-100, LNM 1321 (1988)
YAN, Jia-An
A formula for densities of transition functions
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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
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XXIII: 32, 393-394, LNM 1372 (1989)
YAN, Jia-An
Sur la transformée de Fourier de H. H. Kuo
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XXIII: 33, 395-404, LNM 1372 (1989)
YAN, Jia-An
Generalizations of Gross' and Minlos' theorems
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XXV: 08, 61-78, LNM 1485 (1991)
MEYER, Paul-André; YAN, Jia-An
Les fonctions caractéristiques'' des distributions sur l'espace de Wiener
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XXV: 09, 79-94, LNM 1485 (1991)
YAN, Jia-An
Notes on the Wiener semigroup and renormalization
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XXV: 10, 95-107, LNM 1485 (1991)
YAN, Jia-An
Some remarks on the theory of stochastic integration
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XXV: 36, 427-427, LNM 1485 (1991)
YAN, Jia-An
Correction au Séminaire XXIII
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XXX: 08, 104-107, LNM 1626 (1996)
YAN, Jia-An
An asymptotic evaluation of heat kernel for short time
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XXXII: 06, 56-66, LNM 1686 (1998)
STRICKER, Christophe; YAN, Jia-An
Some remarks on the optional decomposition theorem
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