TOPOLOGICAL EQUIVALENCE FOR DISCONTINUOUS RANDOM DYNAMICAL SYSTEMS AND APPLICATIONS
2013 ◽
Vol 14
(01)
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pp. 1350007
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Keyword(s):
After defining non-Gaussian Lévy processes for two-sided time, stochastic differential equations with such Lévy processes are considered. Solution paths for these stochastic differential equations have countable jump discontinuities in time. Topological equivalence (or conjugacy) for such an Itô stochastic differential equation and its transformed random differential equation is established. Consequently, a stochastic Hartman–Grobman theorem is proved for the linearization of the Itô stochastic differential equation. Furthermore, for Marcus stochastic differential equations, this topological equivalence is used to prove the existence of global random attractors.
2015 ◽
Vol 52
(01)
◽
pp. 149-166
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2015 ◽
Vol 52
(1)
◽
pp. 149-166
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2016 ◽
Vol 17
(05)
◽
pp. 1750033
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2019 ◽
Vol 37
(6)
◽
pp. 1028-1041
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2009 ◽
Vol 22
(1)
◽
pp. 122-136
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