×

zbMATH — the first resource for mathematics

S p stability of solutions of symmetric stochastic differential equations with discontinuous driving semimartingales. (English) Zbl 0636.60057
The paper studies the stability of a solution of a multidimensional symmetric (Stratonovich) stochastic integral equation of the type \[ X_ t=x+\int^{t}_{0}f(X_{s-})dZ_ s, \] when the driving cadlag semi- martingale Z is perturbed in S p (S p, \(1\leq p\leq \infty\), is the Banach space of all cadlag processes \(X=(X_ t)\), \(t\leq T\), such that \(\| X\|_{S\quad p}=\| \sup_{t\leq T}| X_ t| \|_{L\quad p}<\infty)\).
Reviewer: L.Gal’čuk

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93E15 Stochastic stability in control theory
PDF BibTeX XML Cite
Full Text: Numdam EuDML