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In Markov Decision Processes (MDPs) with intermittent state information, decision-making becomes challenging due to periods of missing observations. Linear programming (LP) methods can play a crucial role in solving MDPs, in particular,…
The dynamical evolution of spatial patterns in a complex system can reveal the underlying structure and stability of stationary states. As a model system we employ a two-component rubidium Bose-Einstein condensate at the transition from…
Markov chains provide a foundational framework for modeling sequential stochastic processes, with the transition probability matrix characterizing the dynamics of state evolution. While classical estimation methods such as maximum…
We consider a robust approach to address uncertainty in model parameters in Markov Decision Processes (MDPs), which are widely used to model dynamic optimization in many applications. Most prior works consider the case where the uncertainty…
Because failures in distribution systems caused by extreme weather events directly result in consumers' outages, this paper proposes a state-based decision-making model with the objective of mitigating loss of load to improve the…
The foundations of statistical mechanics, namely how equilibrium hypothesis emerges microscopically from quantum theory, is explored through investigating the environment-induced quantum decoherence processes. Based on the recent results on…
One calls attention to the fact that the stochastic physical systems are not random completely. They have both random and regular components of their evolution. Dynamic system is considered to be a special case of physical system with…
We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such…
Dynamic and evolving operational and economic environments present significant challenges for decision-making. We explore a simulation optimization problem characterized by non-stationary input distributions with regime-switching dynamics…
We consider a stochastic individual based model where each predator searches during a random time and then manipulates its prey or rests. The time distributions may be non-exponential. An age structure allows to describe these interactions…
A novel method for stability and instability study of autonomous dynamical systems using the flow and divergence of the vector field is proposed. A relation between the method of Lyapunov functions and the proposed method is established.…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high…
We establish convergence to an invariant measure as time tends to infinity, for a large class of (possibly non-Markovian) stochastic volatility models. Our arguments are based on a novel coupling idea for Markov chains which also extends to…
This paper deals with nonlinear mechanics of an elevator brake system subjected to uncertainties. A deterministic model that relates the braking force with uncertain parameters is deduced from mechanical equilibrium conditions. In order to…
We consider a non-atomic congestion game where each decision maker performs selfish optimization over states of a common MDP. The decision makers optimize for their own expected costs, and influence each other through congestion effects on…
Bursty dynamics characterizes systems that evolve through short active periods of several events, which are separated by long periods of inactivity. Systems with such temporal heterogeneities are not only found in nature but also include…
We propose a moving horizon estimation scheme to estimate the states and the unknown constant parameters of general nonlinear uncertain discrete-time systems. The proposed framework and analysis explicitly do not involve the a priori…
Srinivas [Commun. Math. Phys. 71 (1980), 131-158] proposed a postulate in quantum mechanics that extends the von Neumann-Lueders collapse postulate to observables with continuous spectrum. His collapse postulate does not determine a unique…
Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…