TY - CHAP
T1 - Stochastic Stability
AU - Schuss, Zeev
N1 - Publisher Copyright:
© 2010, Springer Science+Business Media, LLC.
PY - 2010
Y1 - 2010
N2 - The notion of stability in deterministic and stochastic systems is not the same. The solution of a deterministic system of differential equations (11.1) is stable if for any positive number there exist two numbers, and, such that for any solution of (11.1) whenever (11.2) for some. The solution is said to be asymptotically stable if it is stable and, in addition, (11.3) for any solution satisfying (11.2). If eq. (11.3) holds for all solutions of eq. (11.1), then is said to be globally stable.
AB - The notion of stability in deterministic and stochastic systems is not the same. The solution of a deterministic system of differential equations (11.1) is stable if for any positive number there exist two numbers, and, such that for any solution of (11.1) whenever (11.2) for some. The solution is said to be asymptotically stable if it is stable and, in addition, (11.3) for any solution satisfying (11.2). If eq. (11.3) holds for all solutions of eq. (11.1), then is said to be globally stable.
KW - Colored Noise
KW - Equilibrium Point
KW - Inverted Pendulum
KW - Stability Criterion
KW - Stochastic Stability
UR - http://www.scopus.com/inward/record.url?scp=85067933141&partnerID=8YFLogxK
U2 - 10.1007/978-1-4419-1605-1_11
DO - 10.1007/978-1-4419-1605-1_11
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AN - SCOPUS:85067933141
T3 - Applied Mathematical Sciences (Switzerland)
SP - 399
EP - 441
BT - Applied Mathematical Sciences (Switzerland)
PB - Springer
ER -