×

On the approximation of stochastic differential equation and on Stroock- Varadhan’s support theorem. (English) Zbl 0711.60051

The celebrated Stroock-Varadhan’s support theorem for diffusions is extended to the following case: \(x_ t\) is a solution of the stochastic differential equation \[ dx_ t=b(t,x_ t)dt+\sum^{l}_{i=1}\sigma_ i(t,x_ t)\circ dm^ i_ t, \] where \(m_ t\) is a continuous semimartingale, b and \(\sigma\) are supposed to be unbounded, Lipschitz continuous and with at most linear growth. Under additional technical assumptions, the author gives the complete description of the support of the law of \(x_ t\).
Reviewer: M.Chaleyat-Maurel

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Gyöngy, I., On the Approximation of Stochastic Differential Equations, Stochastics, 23, 331-352 (1988) · Zbl 0635.60071
[5] Ikeda, N.; Watanabe, S., Sochastic Differential equations and Diffusion Processes (1981), North - Holland - Kodanska: North - Holland - Kodanska Amsterdam - Tokyo
[6] Mackevicius, V., \(S^P\) stability of symmetric stochastic differential equations, Lietuvos Matematikos Rinkinys, 25, 72-84 (1985), (In Russian) · Zbl 0588.60050
[7] Mackevicius, V., On the support of the solution of stochastic differential equations, Lietuvos Matematikos Rinkinys, 25, 91-98 (1986), (in Russian)
[8] Mackevicius, V., \(S^P\) stability of solutions of symmetric stochastic differential equations with discontinuous driving semimartingales, Ann. Inst. Henri Poincaré, 23, 575-592 (1987) · Zbl 0636.60057
[9] Picard, J., Method de perturbation pour les equations differentiales stochastiques et le filtrage non lineaire, (These (1987), Université de Province Centre Saint-Charles)
[10] Strook, D. W.; Varadhan, S. R.S., On the Support of Diffusion Progcsses with Applications to Strong Maximum Principle, (Proc. Sixth Berkeley Symp. Math. Statist. Prob., III (1972), University of California Press: University of California Press Berkeley), 333-359
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.