Pathwise Stability of Degenerate Stochastic Evolutions |
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Authors: | Joris Bierkens |
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Institution: | 1.Centrum Wiskunde & Informatica,Amsterdam,The Netherlands |
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Abstract: | For linear stochastic evolution equations with linear multiplicative noise, a new method is presented for estimating the pathwise
Lyapunov exponent. The method consists of finding a suitable (quadratic) Lyapunov function by means of solving an operator
inequality. One of the appealing features of this approach is the possibility to show stabilizing effects of degenerate noise.
The results are illustrated by applying them to the examples of a stochastic partial differential equation and a stochastic
differential equation with delay. In the case of a stochastic delay differential equation our results improve upon earlier
results. |
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Keywords: | |
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