Abstract
This paper presents an analytic technique to derive time-dependent bounds on solutions of nonlinear continuous-time systems which are perturbed by real noise processes. The technique provides a tool to analyze the transient behavior of such systems. Moreover, it can also be used to study the quantitative behavior of sample paths of stochastic nonlinear systems. For instance, one can obtain lower bounds on first hitting times, estimate first exit times, and prove boundedness of sample paths. Our approach, originating from the theory of random attractors, is similar to Lyapunov’s direct method.
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Schenk-Hoppé, K.R. (2001). Bounds on Sample Paths of Stochastic Nonlinear Systems — A Lyapunov Function Approach. In: Narayanan, S., Iyengar, R.N. (eds) IUTAM Symposium on Nonlinearity and Stochastic Structural Dynamics. Solid Mechanics and its Applications, vol 85. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0886-0_20
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DOI: https://doi.org/10.1007/978-94-010-0886-0_20
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3808-9
Online ISBN: 978-94-010-0886-0
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