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@article{Engel:2019:tran/7803,
author = {Engel, M and Lamb, J and Rasmussen, M},
doi = {tran/7803},
journal = {Transactions of the American Mathematical Society},
pages = {6343--6370},
title = {Conditioned Lyapunov exponents for random dynamical systems},
url = {http://dx.doi.org/10.1090/tran/7803},
volume = {372},
year = {2019}
}

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TY  - JOUR
AB  - We introduce the notion of Lyapunov exponents for random dynamical systems, conditioned to tra-jectories that stay within a bounded domain for asymptotically long times.  This is motivated by thedesire to characterize local dynamical properties in the presence of unbounded noise (when almost alltrajectories are unbounded).  We illustrate its use in the analysis of local bifurcations in this context.The  theory  of  conditioned  Lyapunov  exponents  of  stochastic  differential  equations  builds  on  thestochastic analysis of quasi-stationary distributions for killed processes and associated quasi-ergodic dis-tributions.  We show that conditioned Lyapunov exponents describe the asymptotic stability behaviourof  trajectories  that  remain  within  a  bounded  domain  and  –  in  particular  –  that  negative  conditionedLyapunov  exponents  imply  local  synchronisation.   Furthermore,  a  conditioned  dichotomy  spectrum  isintroduced and its main characteristics are established.
AU  - Engel,M
AU  - Lamb,J
AU  - Rasmussen,M
DO  - tran/7803
EP  - 6370
PY  - 2019///
SN  - 0002-9947
SP  - 6343
TI  - Conditioned Lyapunov exponents for random dynamical systems
T2  - Transactions of the American Mathematical Society
UR  - http://dx.doi.org/10.1090/tran/7803
UR  - https://www.ams.org/journals/tran/2019-372-09/S0002-9947-2019-07803-0/
UR  - http://hdl.handle.net/10044/1/66356
VL  - 372
ER  -

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