Convergence of stochastic integrals with respect to Hilbert-valued semimartingales
XIE, Yingchao
J. Math. Soc. Japan, Tome 57 (2005) no. 4, p. 735-751 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
For sequences of stochastic integrals $\int _0^\cdot K^n_{s-}dX^n_s$ , functional limit theorems are presented. And stability of strong solutions of stochastic differential equations of type $$X^n=H^n+\int _0^\cdot f(X^n_{s-})dY^n_s, \quad \forall n\geq 1$$ is discussed under jointly weak convergence of driving processes $\{ (H^n,Y^n)\}_{n\geq 1}$ . Where $Y^n$ is an $\bm{H}$ -valued semimartingale, $H^n$ is a $\bm{G}$ -valued càdlàg adapted process, $K^n$ is an ${\mathscr L}(\bm{H},\bm{G})$ -valued càdlàg adapted process and $f:\bm{G}\mapsto {\mathscr L}(\bm{H}, \bm{G})$ satisfies a Lipschitz condition.
Publié le : 2005-07-14
Classification:  convergence of stochastic integrals,  Hilbert-valued semimartingale,  the stability of (SED) with respect to Hilbert-valued semimartingales,  60H05,  60F17,  60G44 
@article{1158241933,
     author = {XIE, Yingchao},
     title = {Convergence of stochastic integrals with respect to Hilbert-valued semimartingales},
     journal = {J. Math. Soc. Japan},
     volume = {57},
     number = {4},
     year = {2005},
     pages = { 735-751},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1158241933}
}

XIE, Yingchao. Convergence of stochastic integrals with respect to Hilbert-valued semimartingales. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp.  735-751. http://gdmltest.u-ga.fr/item/1158241933/