Article
Mathematics, Applied
Xian Chen, Wei Guo, Xu-min Ni
Summary: This study presents a framework for estimating identity by descent (IBD) sharing for a two-population model with migration, utilizing structured coalescent theory and the Kolmogorov backward equation to develop an accurate and robust method for estimating IBD sharing. Simulation studies demonstrate the reliability and accuracy of this approach in population genetics research.
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
(2021)
Review
Multidisciplinary Sciences
Imre Pazsit
Summary: This paper aims to demonstrate that the same random process in stochastic particle theory can be described by two different master equations: a forward and a backward master equation. These two equations show resemblance at the first moment level but become increasingly different with higher moment order. The paper discusses the increasing asymmetry and attributes it to the violation of invariance to time reversal, illustrating with examples.
Article
Mathematics, Interdisciplinary Applications
Mario Lefebvre
Summary: This paper considers a one-dimensional jump-diffusion process Y(t) and a process X(t) defined by dX(t) = p[X(t), Y(t)] dt, where p(·, ·) is a strictly positive or negative function. First-passage-time problems for the degenerate two-dimensional process (X(t), Y(t)) are discussed when the process leaves the continuation region at the latest at the moment of the first jump, and the optimal control problem is also treated. A particular problem, where p[X(t), Y(t)] = Y(t) - X(t) and Y(t) is a standard Brownian motion with jumps, is solved explicitly.
FRACTAL AND FRACTIONAL
(2023)
Article
Statistics & Probability
K. Abdelhadi, N. Khelfallah
Summary: We study backward stochastic differential equations driven by jump Markov processes and establish the theorems of existence, uniqueness, and stability. By constructing a sequence of BSDEJs with globally Lipschitz generators, we approximate the initial problem and prove the existence and uniqueness of solutions. Furthermore, we apply our main results to prove the existence of a unique solution to the Kolmogorov equation of the Markov process.
STOCHASTICS AND DYNAMICS
(2022)
Article
Mathematics
Oluseyi Odubote, Daniel F. Linder
Summary: This study explores estimating equations for the reaction rate parameters of density dependent Markov jump processes (DDMJP) using variance-covariance weights obtained from an approximating process. The proposed methodology's performance is investigated through simulation of the Lotka-Volterra predator-prey model and fitting a susceptible, infectious, removed (SIR) model to real data from the historical plague outbreak in Eyam, England.
Article
Automation & Control Systems
Jun Moon
Summary: This paper investigates the linear-quadratic (LQ) leader-follower Stackelberg differential game for Markov jump-diffusion stochastic differential equations (SDEs). By using the general stochastic maximum principle and the Four-Step Scheme, the optimal solutions for the leader and the follower are obtained in terms of coupled Riccati differential equations (CRDEs). The well-posedness of the CRDEs is demonstrated, and numerical simulations are conducted to verify the results. (c) 2022 Elsevier Ltd. All rights reserved.
Review
Mathematics, Applied
S. Redner
Summary: This study used the backward Kolmogorov equation approach to explore the paradoxical feature that the mean waiting time for encountering distinct fixed-length sequences of heads and tails during repeated fair coin flips can be different. Results for sequences of lengths 3, 4, and 5 were provided, with extension to longer sequences straightforward. Moment generating functions were derived to find any moment of the mean waiting time for specific sequences.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
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
Mathematics, Applied
Na Li, Jie Xiong, Zhiyong Yu
Summary: In this study, a kind of linear-quadratic Stackelberg games with multilevel hierarchy driven by both Brownian motion and Poisson processes is considered. The Stackelberg equilibrium is presented by linear forward-backward stochastic differential equations (FBSDEs) with Poisson processes (FBSDEPs) in a closed form, and the unique solvability of FBSDEPs with a multilevel self-similar domination-monotonicity structure is obtained using the continuity method.
SCIENCE CHINA-MATHEMATICS
(2021)
Article
Automation & Control Systems
Wenjing Wang, Juanjuan Xu, Huanshui Zhang
Summary: This paper investigates the exact controllability of forward and backward stochastic difference systems with multiplicative noise. By transforming the system into an equivalent backward stochastic difference equation, the necessary and sufficient Gramian matrix criterion and Rank criterion for the exact controllability of the system are derived.
Article
Computer Science, Artificial Intelligence
Damjan Skulj
Summary: This paper proposes a numerical approach to computing solutions of a generalized Kolmogorov backward equation using a nonlinear operator obtained as the lower bound of a set of stochastic matrices. The paper aims to develop a more efficient approach by reducing the number of optimization steps required for the prescribed accuracy of the solutions. Initial tests show that it significantly outperforms existing methods in most cases.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2023)
Article
Mathematics, Applied
Mario Lefebvre
Summary: The study focuses on the impact of Wiener processes with different mean values on X(0) and investigates the probability density function when X(t) equals 0.
STOCHASTIC ANALYSIS AND APPLICATIONS
(2022)
Article
Statistics & Probability
Alexander Dunlap, Yu Gu
Summary: This article considers a nonlinear stochastic heat equation in spatial dimension d = 2, forced by a white-in-time multiplicative Gaussian noise with spatial correlation lengths epsilon > 0 but divided by a factor of root log epsilon(-1). We impose a condition on the Lipschitz constant of the nonlinearity so that the problem is in the weak noise regime. It is shown that as epsilon tends to zero, the one-point distribution of the solution converges, with the limit characterized in terms of the solution to a forward-backward stochastic differential equation (FBSDE). The limiting multipoint statistics of the solution are also characterized using similar terms when the points are chosen on appropriate scales. Our approach is novel even for the linear case, where the FBSDE can be explicitly solved, and we recover the results of Caravenna, Sun, and Zygouras.
ANNALS OF PROBABILITY
(2022)
Article
Statistics & Probability
Mario Lefebvre
Summary: Consider a one-dimensional diffusion process Y(t) satisfying the differential equation dX(t) = -Y(t) dt. Let t(x, y) be the first time the process (X(t), Y(t)), starting from (x, y), leaves a subset of the first quadrant. This paper studies the problem of computing the probability p(x, y) := P[X(t(x, y)) = 0]. The Laplace transform of the function p(x, y) is derived in important special cases, and it is shown that the transform can be numerically inverted. Explicit expressions for the Laplace transform of E[t(x, y)] and the moment-generating function of t(x, y) can also be obtained.
JOURNAL OF APPLIED PROBABILITY
(2023)
Article
Automation & Control Systems
K. A. Vytovtov, E. A. Barabanova
Summary: The article examines an inhomogeneous Markov process with finitely many discrete states, continuous time, and piecewise constant transition intensities. Analytical expressions for both transient and steady-state modes of the random process are presented for the first time. Results of numerical calculations for processes without jumps, with jumps, and with periodic jumps in transition intensities are provided.
AUTOMATION AND REMOTE CONTROL
(2021)
Article
Engineering, Electrical & Electronic
Rajesh Joshi, Manasa Mandava, Girish P. Saraph
IETE TECHNICAL REVIEW
(2008)
Proceedings Paper
Computer Science, Information Systems
A. Bagula, C. Lubamba, M. Mandava, H. Bagula, M. Zennaro, E. Pietrosemoli
PROCEEDINGS OF THE 2016 ITU KALEIDOSCOPE ACADEMIC CONFERENCE - ICTS FOR A SUSTAINABLE WORLD (ITU WT)
(2016)
Proceedings Paper
Automation & Control Systems
Eugene A. Feinberg, Manasa Mandava, Albert N. Shiryaev
2013 IEEE 52ND ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC)
(2013)
Article
Mathematics, Applied
Geunsu Choi, Mingu Jung, Sun Kwang Kim, Miguel Martin
Summary: This paper studies weak-star quasi norm attaining operators and proves that the set of such operators is dense in the space of bounded linear operators regardless of the choice of Banach spaces. It is also shown that weak-star quasi norm attaining operators have distinct properties from other types of norm attaining operators, although they may share some equivalent properties under certain conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maria Lorente, Francisco J. Martin-Reyes, Israel P. Rivera-Rios
Summary: In this paper, we provide quantitative one-sided estimates that recover the dependences in the classical setting. We estimate the one-sided maximal function in Lorentz spaces and demonstrate the applicability of the conjugation method for commutators in this context.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Fernando Cobos, Luz M. Fernandez-Cabrera
Summary: We provide a necessary and sufficient condition for the weak compactness of bilinear operators interpolated using the real method. However, this characterization does not hold for interpolated operators using the complex method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ovgue Gurel Yilmaz, Sofiya Ostrovska, Mehmet Turan
Summary: The Lupas q-analogue Rn,q, the first q-version of the Bernstein polynomials, was originally proposed by A. Lupas in 1987 but gained popularity 20 years later when q-analogues of classical operators in approximation theory became a focus of intensive research. This work investigates the continuity of operators Rn,q with respect to the parameter q in both the strong operator topology and the uniform operator topology, considering both fixed and infinite n.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
M. Agranovsky, A. Koldobsky, D. Ryabogin, V. Yaskin
Summary: This article modifies the concept of polynomial integrability for even dimensions and proves that ellipsoids are the only convex infinitely smooth bodies satisfying this property.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Abel Komalovics, Lajos Molnar
Summary: In this paper, a parametric family of two-variable maps on positive cones of C*-algebras is defined and studied from various perspectives. The square roots of the values of these maps under a faithful tracial positive linear functional are considered as a family of potential distance measures. The study explores the problem of well-definedness and whether these distance measures are true metrics, and also provides some related trace characterizations. Several difficult open questions are formulated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Frederic Bayart
Summary: The passage describes the construction of an operator on a separable Hilbert space that is 5-hypercyclic for all δ in the range (ε, 1) and is not 5-hypercyclic for all δ in the range (0, ε).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Helene Frankowska, Nikolai P. Osmolovskii
Summary: This paper investigates second-order optimality conditions for the minimization problem of a C2 function f on a general set K in a Banach space X. Both necessary and sufficient conditions are discussed, with the sufficiency condition requiring additional assumptions. The paper demonstrates the validity of these assumptions for the case when the set K is an intersection of sets described by smooth inequalities and equalities, such as in mathematical programming problems. The novelty of the approach lies in the arbitrary nature of the set K and the straightforward proofs.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ole Fredrik Brevig, Kristian Seip
Summary: This paper studies the Hankel operator on the Hardy space and discusses its minimal and maximal norms, as well as the relationship between the maximal norm and the properties of the function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Alexander Meskhi
Summary: Rubio de Francia's extrapolation theorem is established for new weighted grand Morrey spaces Mp),lambda,theta w (X) with weights w beyond the Muckenhoupt Ap classes. This result implies the one-weight inequality for operators of Harmonic Analysis in these spaces for appropriate weights. The necessary conditions for the boundedness of the Hardy-Littlewood maximal operator and the Hilbert transform in these spaces are also obtained. Some structural properties of new weighted grand Morrey spaces are investigated. Problems are studied in the case when operators and spaces are defined on spaces of homogeneous type.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maud Szusterman
Summary: In this work, the necessary conditions on the structure of the boundary of a convex body K to satisfy all inequalities are investigated. A new solution for the 3-dimensional case is obtained in particular.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Rami Ayoush, Michal Wojciechowski
Summary: In this article, lower bounds for the lower Hausdorff dimension of finite measures are provided under certain restrictions on their quaternionic spherical harmonics expansions. This estimate is analogous to a result previously obtained by the authors for complex spheres.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
F. G. Abdullayev, V. V. Savchuk
Summary: This paper investigates the convergence and theorem proof of the Takenaka-Malmquist system and Fejer-type operator on the unit circle, and provides relevant results on the class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Sofiya Ostrovska, Mikhail I. Ostrovskii
Summary: This work aims to establish new results on the structure of transportation cost spaces. The main outcome of this paper states that if a metric space X contains an isometric copy of L1 in its transportation cost space, then it also contains a 1-complemented isometric copy of $1.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Pilar Rueda, Enrique A. Sanchez Perez
Summary: We prove a factorization theorem for Lipschitz operators acting on certain subsets of metric spaces of measurable functions and with values on general metric spaces. Our results show how a Lipschitz operator can be extended to a subset of other metric space of measurable functions that satisfies the following optimality condition: it is the biggest metric space, formed by measurable functions, to which the operator can be extended preserving the Lipschitz constant. Also, we demonstrate the coarsest metric that can be given for a metric space in which an order bounded lattice-valued-Lipschitz map is defined, and provide concrete examples involving the relevant space L0(mu).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)