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Lyapunov exponents and stochastic flows of linear and affine hereditary systems. (English) Zbl 0763.60030
Diffusion processes and related problems in analysis, Vol. II: Stochastic flows, Proc. Conf. Charlotte/NC (USA) 1990, Prog. Probab. 27, 141-169 (1992).

[For the entire collection see Zbl 0742.00084.]

The author reviews recent results concerning stochastic linear functional equations driven by semimartingales. The main attention is devoted to the existence of solutions which are continuous linear transformations of the initial data and to the stability of solutions via characterization of the Lyapunov exponents with respect to natural norms on the state space.


MSC:
60H10Stochastic ordinary differential equations