M. Shub, B. Weiss
Ergodic Theory and Dynamical Systems
The study of density-dependent stochastic population processes (DDSPPs) is important from a historical perspective as well as from the perspective of a number of existing and emerging applications today. In more recent applications of these processes, it can be especially important to include time-varying parameters for the rates that impact the density-dependent population structures and behaviors. Under a mean-field scaling, we show that such time-inhomogeneous DDSPPs converge to a corresponding nonautonomous dynamical system. We then analogously establish that the optimal control of such time-inhomogeneous DDSPPs converges to the optimal control of the limiting dynamical system. An analysis of both the dynamical system and its optimal control renders various important mathematical properties of interest.
M. Shub, B. Weiss
Ergodic Theory and Dynamical Systems
S.F. Fan, W.B. Yun, et al.
Proceedings of SPIE 1989
Joy Y. Cheng, Daniel P. Sanders, et al.
SPIE Advanced Lithography 2008
Michael Ray, Yves C. Martin
Proceedings of SPIE - The International Society for Optical Engineering