Necessary and sufficient conditions for near-optimality in stochastic control of FBSDEs

2009 ◽  
Vol 58 (12) ◽  
pp. 857-864 ◽  
Author(s):  
Khaled Bahlali ◽  
Nabil Khelfallah ◽  
Brahim Mezerdi
Keyword(s):  
Stochastic Control ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
Near Optimality

scholarly journals Lyapunov Characterization for the Stability of Stochastic Control Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Fakhreddin Abedi ◽  
Wah June Leong ◽  
Mohammad Abedi
Keyword(s):  
Control Systems ◽  
Stochastic Control ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Stability ◽  
Necessary And Sufficient

Lyapunov-like characterization for the problem of input-to-state stability in the probability of nonautonomous stochastic control systems is established. We extend the well-known Artstein-Sontag theorem to derive the necessary and sufficient conditions for the input-to-state stabilization of stochastic control systems. Illustrating example is provided.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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