TY - GEN A1 - Winkelmann, Stefanie T1 - Markov Control with Rare State Observation: Average Optimality N2 - This paper investigates the criterion of long-term average costs for a Markov decision process (MDP) which is not permanently observable. Each observation of the process produces a fixed amount of \textit{information costs} which enter the considered performance criterion and preclude from arbitrarily frequent state testing. Choosing the \textit{rare} observation times is part of the control procedure. In contrast to the theory of partially observable Markov decision processes, we consider an arbitrary continuous-time Markov process on a finite state space without further restrictions on the dynamics or the type of interaction. Based on the original Markov control theory, we redefine the control model and the average cost criterion for the setting of information costs. We analyze the constant of average costs for the case of ergodic dynamics and present an optimality equation which characterizes the optimal choice of control actions and observation times. For this purpose, we construct an equivalent freely observable MDP and translate the well-known results from the original theory to the new setting. T3 - ZIB-Report - 16-59 KW - Markov decision process KW - partial observability KW - average optimality KW - information costs Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-60981 SN - 1438-0064 ER - TY - GEN A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - The spatiotemporal master equation: approximation of reaction-diffusion dynamics via Markov state modeling N2 - Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest. We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments and diffusive motion is approximated by jumps between these compartments. Treating these jumps as first-order reactions, simulation of the resulting stochastic system is possible by the Gillespie method. We present the theory of Markov state models (MSM) as a theoretical foundation of this intuitive approach. By means of Markov state modeling, both the number and shape of compartments and the transition rates between them can be determined. We consider the ST-CME for two reaction-diffusion systems and compare it to more detailed models. Moreover, a rigorous formal justification of the ST-CME by Galerkin projection methods is presented. T3 - ZIB-Report - 16-60 KW - reaction-diffusion KW - stochastic chemical kinetics KW - chemical master equation Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-60999 SN - 1438-0064 ER -