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
Mathematics
Khrystyna Prysyazhnyk, Iryna Bazylevych, Ludmila Mitkova, Iryna Ivanochko
Summary: The study focuses on the homogeneous branching process with migration and continuous time, investigating the distribution of period-life tau and obtaining the probability generating function of the random process. Additionally, the boundary theorem for the period-life of the subcritical or critical branching process with migration was identified.
Article
Automation & Control Systems
Xue Song, Shuping Ma
Summary: This paper discusses the ILQ optimal control problem for continuous-time linear rectangular DMJSs and transforms it into a standard LQ problem for MJSs. The solvable conditions and non-negative optimal cost value are obtained. The effectiveness of the methods is illustrated through numerical examples.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
(2022)
Article
Statistics & Probability
Matyas Barczy, Sandra Palau, Gyula Pap
Summary: Under certain moment conditions on the branching and immigration mechanisms, this study demonstrates the asymptotic mixed normality of a scaled projection of a supercritical and irreducible continuous-state and continuous-time branching process with immigration on specific left non-Perron eigenvectors of the branching mean matrix. Additionally, asymptotic normality is proven under some conditional probability measure, along with the convergence of relative frequencies of distinct types of individuals on a suitable event.
ADVANCES IN APPLIED PROBABILITY
(2021)
Article
Engineering, Chemical
Qiankun Zhao, Lixia Yang, Chaoqun Yao, Guangwen Chen
Summary: An ultrasound-assisted tube crystallization device was developed for continuous antisolvent crystallization of acetylsalicylic acid. Results showed that the device had high energy efficiency and excellent temperature control. The effects of ultrasonic power, time, supersaturation degree, and excitation method on the crystallization process were investigated. The improved device demonstrated superior performance compared to conventional crystallizers.
INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH
(2023)
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
Mathematics
Shukai Chen, Zenghu Li
Summary: In this study, a continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes. The distribution of local jumps is derived from the stochastic equation system, and exponential ergodicity in Wasserstein-type distances of the transition semigroup is established. Immigration structures associated with the process are also investigated, along with the existence of the stationary distribution of the process with immigration.
ACTA MATHEMATICA SCIENTIA
(2021)
Article
Automation & Control Systems
Xue Song, Shuping Ma
Summary: The indefinite linear quadratic (ILQ) optimal control problem for continuous-time descriptor Markov jump systems (DMJSs) is discussed in this work. Firstly, the ILQ problem of DMJSs is transformed into the standard LQ problem of Markov jump systems (MJSs) with some inequality and rank conditions using elementary linear algebra approach. Then, based on the LQ theory of MJSs, a sufficient condition for the solvability of the ILQ problem for DMJSs is obtained. The optimal state feedback control and the nonnegative optimal cost value are derived, and the resulting closed-loop system is stochastically admissible. Finally, a numerical example is provided to validate the effectiveness of the presented methods.
INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS
(2023)
Article
Engineering, Electrical & Electronic
Yufeng Tian, Zhanshan Wang, Changlai Wang
Summary: This paper investigates the H-infinity state estimation problem of continuous-time delayed nonhomogeneous Markov jump systems and proposes a switched vertices approach to relax the bound assumptions, resulting in more practical results.
CIRCUITS SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Statistics & Probability
Romain Abraham, Jean-Francois Delmas, Hui He
Summary: The study examines the genealogical tree of a stationary continuous state branching process with immigration, establishing distributions under various stable branching mechanisms and analyzing the number of individuals in the extant population who will produce descendants in the future. The transition rates of the associated Markov processes were computed to determine their characteristics.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2021)
Article
Statistics & Probability
Dawei Lu, Huangding Lv
Summary: This paper investigates a special class of population-size-dependent branching processes, which can be viewed as an extension of Galton-Watson processes with state-dependent immigration. The model considers the size of individuals in each generation and evolves according to different Galton-Watson processes or fixed immigration distributions. By using technical results from Foster (1971) and Pakes (1971), asymptotic results similar to those of Galton-Watson processes with state-dependent immigration are obtained through detailed computations.
STATISTICS & PROBABILITY LETTERS
(2023)
Article
Automation & Control Systems
Chiwoo Park
Summary: This paper presents a Gaussian process model for estimating piecewise continuous regression functions. Unlike conventional GP regression methods, this approach partitions the local data into pieces using a local data partitioning function to improve modeling flexibility. The advantages of using this approach over traditional methods are demonstrated through various experiments and data studies.
JOURNAL OF MACHINE LEARNING RESEARCH
(2022)
Article
Mathematics, Interdisciplinary Applications
Khaoula Abdelhadi, Mhamed Eddahbi, Nabil Khelfallah, Anwar Almualim
Summary: This article deals with backward stochastic differential equations driven by a pure jump Markov process and an independent Brownian motion (BSDEJs). We first prove the existence and uniqueness of solutions for this type of equation and provide a comparison of solutions in the case of Lipschitz conditions in the generator. With these tools, we study the existence of a (minimal) solution for BSDE where the coefficient is continuous and satisfies the linear growth condition. An existence result for BSDE with a left-continuous, increasing, and bounded generator is also discussed. Finally, the general result is applied to solve one kind of quadratic BSDEJ.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics
Istvan Fazekas, Attila Barta
Summary: A continuous-time network evolution model based on 2- and 3-interactions is considered, with the evolution of the edges and triangles governed by a multi-type continuous-time branching process. The study focuses on the limiting behavior of the network, proving that the number of triangles and edges have the same magnitude on the event of non-extinction. The probability of extinction and degree process of a fixed vertex are also studied, with results illustrated by simulations.
Article
Mathematics, Applied
Romeo Awi, Ryan Hynd, Henok Mawi
Summary: In this paper, we discuss the problem of approximating the Nash equilibria of N functions f(1), ..., f(N) of N variables. Specifically, we prove that the systems of the form u(j)(t) = -λ(xj)f(j)(u(t))(j = 1, ..., N) are well-posed and the large time limits of their solutions u(t) = (u1(t), ..., uN(t)) are Nash equilibria for f(1), ..., f(N), under the condition that these functions satisfy an appropriate monotonicity condition. For this purpose, we employ the theory of maximal monotone operators on a Hilbert space. We also explore the application of these ideas in game theory and provide a method to approximate equilibria in certain game theoretic problems in function spaces.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2023)
