Article
Economics
Minsoo Jeong
Summary: This paper presents a novel approach to model financial time series that captures both persistency and long term stationarity. The provided statistical theory and empirical evidence support the existence and characteristic behavior of such series in real financial data.
ECONOMIC MODELLING
(2022)
Article
Engineering, Electrical & Electronic
Daniel Chen, Alexander G. Strang, Andrew W. Eckford, Peter J. Thomas
Summary: This paper presents a continuous-time formulation of the sum-product algorithm for inferring the conditional probabilities of hidden states in a system. The algorithm, based on finite, discrete-time observations, explicitly solves for the conditional probability of occupying any state given the transition rates and observations within a finite time window.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2022)
Article
Mathematics, Applied
Stefan Ankirchner, Thomas Kruse, Mikhail Urusov
Summary: The paper discusses the convergence speed of a numerical scheme for approximating one-dimensional continuous strong Markov processes, proving that the approximating Markov chains converge at a rate of 1/4 with respect to every p-th Wasserstein distance at fixed times. It also examines the convergence of paths with any rate strictly smaller than 1/4. The results are applicable to processes with irregular behavior, such as solutions of SDEs with irregular coefficients and processes with sticky points.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics
Manuel L. Esquivel, Nadezhda P. Krasii, Gracinda R. Guerreiro
Summary: This study addresses the problem of finding a natural continuous time Markov type process in open populations using information provided by discrete time open Markov chains. Two main approaches are proposed: calibrating a continuous time Markov process using a discrete time transition matrix and directly extending discrete time theory to continuous time theory using semi-Markov processes and open Markov schemes.
Article
Mathematics, Applied
Mengyuan Chen, Yan Zhang, Zhang Zhang, Lun Du, Shuo Wang, Jiang Zhang
Summary: Network structures are crucial in various systems, but real cases often have incomplete or unavailable observable nodes and connections. This paper proposes a data-driven deep learning model called GIN, which infers the unknown parts of a network structure and the initial states of observable nodes using time series data from network dynamics. Experimental results demonstrate up to 90% accuracy in inferring the unknown parts and linear accuracy decline with the increase of unobservable nodes. This framework has wide applications when network structure is hard to obtain and time series data is rich.
Article
Operations Research & Management Science
Eugene Feinberg, Manasa Mandava, Albert N. Shiryaev
Summary: This article investigates the solutions of Kolmogorov's backward and forward equations for jump Markov processes. The authors found that the minimal solution is the transition probability if the transition rate is bounded. The paper also presents more general results, providing sufficient conditions for locally integrable or bounded transition rates.
ANNALS OF OPERATIONS RESEARCH
(2022)
Article
Engineering, Chemical
A. Deser, J. Kuhne
Summary: This article discusses the stochastic nature of charging in aerosol particles, utilizing the framework of continuous time Markov processes to analyze the principles of charging and introducing a novel numerical method for calculating the time evolution of charging processes. Additionally, the application of ergodicity is used to determine stationary charge distributions in the case of bipolar charging in finite state-space Markov processes.
JOURNAL OF AEROSOL SCIENCE
(2021)
Article
Physics, Multidisciplinary
Andreas Dechant
Summary: In this study, we investigate the problem of minimizing the entropy production for a physical process described by Markov jump dynamics. We find that, without any additional constraints, a given time-evolution can be realized with arbitrarily small entropy production at the expense of diverging activity. However, when the activity is fixed, the dynamics that minimizes the entropy production is driven by conservative forces. Moreover, we express the value of the minimum entropy production in terms of the graph-distance based Wasserstein distance between the initial and final configuration, which introduces a new type of speed limit relating dissipation, the average number of transitions, and the Wasserstein distance. We also demonstrate our findings using simple state networks, a time-dependent pump, and spin flips in the Ising model.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Multidisciplinary
Sarah E. Marzen, James P. Crutchfield
Summary: This paper proposes new methods for inferring, predicting, and estimating continuous-time discrete-event processes. The methods are based on an extension of Bayesian structural inference and utilize the universal approximation power of neural networks. Experimental results on complex synthetic data demonstrate that these methods are competitive with the state-of-the-art for prediction and entropy-rate estimation.
Article
Operations Research & Management Science
Eugene A. Feinberg, Manasa Mandava, Albert N. Shiryaev
Summary: Research shows that in continuous-time jump Markov decision processes, the marginal distributions are equal if the corresponding Markov policy defines a nonexplosive jump Markov process. If the Markov process is explosive, the marginal probability at each time instance does not exceed that of the original policy. Additionally, for continuous-time jump Markov decision processes, there exists a Markov policy with the same or better value of the objective function for every policy when the initial state distribution is fixed.
MATHEMATICS OF OPERATIONS RESEARCH
(2021)
Article
Chemistry, Physical
Aljaz Godec, Dmitrii E. Makarov
Summary: In this paper, we discuss the practical challenges of using stochastic thermodynamics to determine the directionality of molecular machines from experimental single-molecule trajectories. Due to the limitations of spatiotemporal resolution in these experiments and the inability to detect both forward and backward transitions between the same states, distinguishing the forward and backward directions of ATP-consuming periodic molecular machines becomes a nontrivial task. By extending the commonly used Markov-state model to analyze single-molecule transition-path measurements, we show how irreversibility can be hidden in these measurements but can be revealed when non-Markov effects in low-dimensional single-molecule trajectories are considered.
JOURNAL OF PHYSICAL CHEMISTRY LETTERS
(2023)
Article
Statistics & Probability
Xin Guo, Yonghui Huang
Summary: This paper discusses risk-sensitive average optimization for denumerable continuous-time Markov decision processes, deriving principles and proving the existence of solutions. It also demonstrates that optimal policies for finite states can approximate those for infinitely countable states.
JOURNAL OF APPLIED PROBABILITY
(2021)
Article
Mathematics
Juan Wang, Xiaojuan Wang
Summary: This article focuses on the large deviation rates of a supercritical continuous-time branching process with immigration and extends the results of the discrete-time Galton-Watson process to the continuous-time case. By proving Z(t) as a submartingale, the decay rates of P(|Z(t) - Z| > epsilon) ast ? infinity and P(|(Y(t + v)/Y(t)) - e(mv)| > epsilon|Z >= alpha) ast ? infinity are studied under various moment conditions.
JOURNAL OF MATHEMATICS
(2022)
Article
Automation & Control Systems
Hongchao Li, Xinzhou Liu, Jiao Liu, Peng Yang
Summary: This paper discusses the stabilization of continuous-time saturating Markov jump system with generally uncertain transition rates (GUTRs) under an event-triggered strategy. An optimization algorithm and stabilization conditions are introduced to achieve the best control effect.
ASIAN JOURNAL OF CONTROL
(2021)
Article
Multidisciplinary Sciences
Phatthamon Kongkhambut, Jim Skulte, Ludwig Mathey, Jayson G. Cosme, Andreas Hemmerich, Hans Kessler
Summary: In this study, we observed a limit cycle phase in a continuously pumped atom-cavity system, characterized by emergent oscillations in the photon number. This dynamical state spontaneously breaks continuous time translation symmetry and is robust against temporal perturbations, demonstrating the realization of a continuous time crystal.