Summary of recent research accomplishments in Markov processes and Markov fields at Wuhan University

Hu, Di He; Liu, Lu Qin; Gao, Fu Qing

doi:10.1090/conm/118/1137967

Cited by 2 publications

(3 citation statements)

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“…Our definition of a pretransition matrix is weaker than that in [3,6,12], but still we can obtain most of the standard results. In particular, the following theorem is essentially the same as Theorem 1.1 and Theorem 1.2 in Chapter 3 of [12]. Theorem 1.…”

Section: Definitionmentioning

confidence: 89%

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Existence and Regularity of a Nonhomogeneous Transition Matrix under Measurability Conditions

Ye¹,

Guo²,

Hernández–Lerma

2008

J Theor Probab

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This paper is about the existence and regularity of the transition probability matrix of a nonhomogeneous continuous-time Markov process with a countable state space. A standard approach to prove the existence of such a transition matrix is to begin with a continuous (in t) and conservative matrix Q(t) = [q ij (t)] of nonhomogeneous transition rates q ij (t), and use it to construct the transition probability matrix. Here we obtain the same result except that the q ij (t) are only required to satisfy a mild measurability condition, and Q(t) may not be conservative. Moreover, the resulting transition matrix is shown to be the minimum transition matrix and, in addition, a necessary and sufficient condition for it to be regular is obtained. These results are crucial in some applications of nonhomogeneous continuous-time Markov processes, such as stochastic optimal control problems and stochastic games, which motivated this work in the first place.

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Section: Definitionmentioning

confidence: 89%

“…In this paper, firstly, we introduce a precise definition of a nonhomogeneous transition matrix (Definition 1), which is weaker than previous definitions, e.g., as in [3,6,12]. Even in this weaker context, we can obtain some key properties of the transition matrix (Theorem 1).…”

Section: Introductionmentioning

confidence: 99%

Existence and Regularity of a Nonhomogeneous Transition Matrix under Measurability Conditions

Ye¹,

Guo²,

Hernández–Lerma

2008

J Theor Probab

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“…In contrast to numerous prior studies [12,[14][15][16][17][18][19], detailed data on patient distribution are frequently overlooked in risk research. In this study, the residential addresses of patients were geographically coded, and fine-grained patient distribution data were obtained as a risk factor, significantly enhancing the scientific foundation of our risk factor analysis [19][20][21][22].…”

Section: Model Advantages and Potential For Large-scale Applicationsmentioning

confidence: 99%

Methods for Infectious Disease Risk Assessments in Megacities Using the Urban Resilience Theory

Wang,

Cao,

et al. 2023

Sustainability

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Since the 20th century began, the world has witnessed the emergence of contagious diseases such as Severe Acute Respiratory Syndrome (SARS), H1N1 influenza, and the recent COVID-19 pandemic. Conducting timely infectious disease risk assessments is of significant importance for preventing the spread of viruses, safeguarding public health, and achieving sustainable development. Most current studies on epidemic risk assessments focus on administrative divisions, making it challenging to reflect the risk disparities within these areas. Taking Shanghai as an example, this research introduces the concept of urban resilience frameworks and identifies the risk factors. By analyzing the interactions among different risk factors using geographic detectors, this study establishes the distribution relationship between the risk factors and newly reported cases using Geographically Weighted Regression. A risk assessment model is constructed to evaluate the infection risk within different regions of the administrative area. The results demonstrate that the central area of Shanghai exhibits the highest infection risk, gradually decreasing toward the periphery. The Spearman’s correlation coefficient (p) between the predicted and actual distribution of new cases reaches 0.869 (p < 0.001), and the coefficient of determination (R2) is 0.938 (p < 0.001), indicating a relatively accurate assessment of infection risk in different spatial areas. This research methodology can be effectively applied to infectious disease risk assessments during public health emergencies, thereby assisting in the formulation of epidemic prevention policies.

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Summary of recent research accomplishments in Markov processes and Markov fields at Wuhan University

Cited by 2 publications

References 0 publications

Existence and Regularity of a Nonhomogeneous Transition Matrix under Measurability Conditions

Existence and Regularity of a Nonhomogeneous Transition Matrix under Measurability Conditions

Methods for Infectious Disease Risk Assessments in Megacities Using the Urban Resilience Theory

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