XVI: 32, 370-379, LNM 920 (1982)
ZHENG, Wei-An
Semimartingales in predictable random open sets
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
XVIII: 13, 154-171, LNM 1059 (1984)
MEYER, Paul-André;
ZHENG, Wei-An
Intégrales stochastiques non monotones Retrieve article from Numdam
XVIII: 14, 172-173, LNM 1059 (1984)
ZHENG, Wei-An
Une remarque sur une même i.s. calculée dans deux filtrations Retrieve article from Numdam
XVIII: 15, 174-178, LNM 1059 (1984)
HE, Sheng-Wu;
ZHENG, Wei-An
Remarques sur la convergence des martingales dans les variétés Retrieve article from Numdam
XVIII: 20, 223-244, LNM 1059 (1984)
ZHENG, Wei-An;
MEYER, Paul-André
Quelques résultats de ``mécanique stochastique'' Retrieve article from Numdam
XVIII: 33, 501-518, LNM 1059 (1984)
ÉMERY, Michel;
ZHENG, Wei-An
Fonctions convexes et semimartingales dans une variété (
Stochastic differential geometry)
On a manifold endowed with a connexion, convex functions can be defined, and transform manifold-valued martingales into real-valued local submartingales (see Darling
1659). This is extended here to the case of non-smooth convex functions. Ii is also shown that they make manifold-valued semimartingales into real semimartingales
Keywords: Semimartingales in manifolds,
Martingales in manifolds,
Convex functionsNature: Original Retrieve article from Numdam
XIX: 02, 12-26, LNM 1123 (1985)
MEYER, Paul-André;
ZHENG, Wei-An
Construction de processus de Nelson réversibles Retrieve article from Numdam
XX: 19, 334-337, LNM 1204 (1986)
MEYER, Paul-André;
ZHENG, Wei-An
Sur la construction de certaines diffusions Retrieve article from Numdam
XXX: 09, 108-116, LNM 1626 (1996)
ZHENG, Wei-An
Meyer's topology and Brownian motion in a composite medium Retrieve article from Numdam
