TY - JOUR
T1 - Almost sure asymptotic stability of scalar stochastic delay equations
T2 - Finite state Markov process
AU - Sri Namachchivaya, N.
AU - Wihstutz, Volker
N1 - Funding Information:
The first author would like to acknowledge the support of the National Science Foundation under grant numbers DMS-0504581 and CMMI-1000906 Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors would also like to thank Mr. Nishanth Lingala for the numerical calculations of the top Lyapunov exponent presented in Sec. 5.4.
PY - 2012/3
Y1 - 2012/3
N2 - In this paper, we study the almost-sure asymptotic stability of scalar delay differential equations with random parametric fluctuations which are modeled by a Markov process with finitely many states. The techniques developed for the determination of almost-sure asymptotic stability of finite dimensional stochastic differential equations will be extended to delay differential equations with random parametric fluctuations. For small intensity noise, we construct an asymptotic expansion for the exponential growth rate (the maximal Lyapunov exponent), which determines the almost-sure stability of the stochastic system.
AB - In this paper, we study the almost-sure asymptotic stability of scalar delay differential equations with random parametric fluctuations which are modeled by a Markov process with finitely many states. The techniques developed for the determination of almost-sure asymptotic stability of finite dimensional stochastic differential equations will be extended to delay differential equations with random parametric fluctuations. For small intensity noise, we construct an asymptotic expansion for the exponential growth rate (the maximal Lyapunov exponent), which determines the almost-sure stability of the stochastic system.
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U2 - 10.1142/S0219493712003560
DO - 10.1142/S0219493712003560
M3 - Article
AN - SCOPUS:84856597908
SN - 0219-4937
VL - 12
JO - Stochastics and Dynamics
JF - Stochastics and Dynamics
IS - 1
M1 - 1150010
ER -