Article
Economics
Bruno Feunou
Summary: We introduce generalized autoregressive positive-valued (GARP) processes, which extend the existing class of autoregressive positive-valued (ARP) processes by incorporating different and identifiable moving averages for the conditional moment dynamics. The article provides ergodicity conditions and closed-form moments for GARP processes, as well as estimation and inference methods. An application to European option pricing demonstrates that GARP processes significantly reduce pricing errors compared to ARP processes.
JOURNAL OF BUSINESS & ECONOMIC STATISTICS
(2023)
Article
Mathematics
Sajid Hussain, Mahmood Ul Hassan, Muhammad Sajid Rashid, Rashid Ahmed
Summary: The study of hydrological characteristics plays a crucial role in water resources design, planning, and management. The selection of appropriate probability distributions and estimation methods are fundamental in hydrology analyses. This article proposes a new family called the 'exponentiated power alpha index generalized' (EPAIG)-G to develop various new distributions. Based on this family, a new model called the EPAIG-exponential (EPAIG-E) is developed, and its structural properties are obtained. The EPAIG-E parameters are estimated using the method of maximum likelihood (MML), and Monte Carlo simulation (MCS) is conducted to assess the model's performance using real data.
Article
Operations Research & Management Science
Rommel G. Regis
Summary: This paper investigates the properties of the cosine measure for a nonempty finite set of nonzero vectors, introduces the concept of the uniform angle subspace and proves some related cone properties, and explores the characteristics of KKT points for the optimization problem of calculating the cosine measure.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2021)
Article
Statistics & Probability
Sonja Cox, Sven Karbach, Asma Khedher
Summary: This paper demonstrates the existence of a broad class of affine Markov processes on the cone of positive self-adjoint Hilbert-Schmidt operators. These processes are well-suited as infinite-dimensional stochastic covariance models. The paper also provides explicit formulas for the first and second moments of the affine processes.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2022)
Article
Statistics & Probability
David Berger, Franziska Kuehn, Rene L. Schilling
Summary: In this paper, new proofs are presented for the existence of generalized moments of a Levy process, along with the equivalent conditions and consequences. The methods can also be extended to moments of stochastically continuous additive processes, and new proofs for the characterization of lattice distributions and the transience of Levy processes are provided.
PROBABILITY AND MATHEMATICAL STATISTICS-POLAND
(2022)
Article
Multidisciplinary Sciences
Areej M. AL-Zaydi
Summary: In this paper, explicit expressions and recurrence relations for the single and product moments of generalized order statistics are provided. These results are used to discuss special cases of generalized order statistics and obtain best linear unbiased estimators. Numerical computations and a real data application are also presented.
Article
Statistics & Probability
B. Chikvinidze
Summary: We establish the necessary and sufficient conditions for the uniform integrability of the stochastic exponential E(M), where M is a continuous local martingale.
JOURNAL OF THEORETICAL PROBABILITY
(2022)
Article
Mathematics, Applied
Huan Zhou, Guang Jun Shen, Qian Yu
Summary: In this paper, we consider the derivatives of intersection local time for two independent d-dimensional symmetric alpha-stable processes and study the sufficient and necessary conditions for their existence. We also investigate the power variation of the derivatives.
ACTA MATHEMATICA SINICA-ENGLISH SERIES
(2023)
Article
Mathematics
Jianhai Bao, Jian Wang
Summary: In this paper, exponential ergodicity under the L-1-Wasserstein distance is established for two-factor affine processes using the coupling approach. The method employed is universal and can be applied to general two-factor affine processes, including those with a general Cox-Ingersoll-Ross (CIR) process as the first component, interactions in the second component, correlated Brownian noises, and even models beyond two-factor processes.
MATHEMATISCHE NACHRICHTEN
(2023)
Article
Mathematics, Applied
B. Chikvinidze
Summary: The paper generalizes the well known mixed Novikov-Kazamaki condition and introduces a new type sufficient condition for the uniform integrability of the stochastic exponential with jumps.
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
(2022)
Article
Statistics & Probability
Serguei Popov, Vadim Shcherbakov, Stanislav Volkov
Summary: This paper focuses on studying the long-term behavior of a competition process, showing that eventually only a random subset of non-interacting components survives while others become extinct. Similar results are also applicable to a related generalized Polya urn model with removals.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2022)
Article
Mathematics, Applied
Huizhong Lin, Liang Wang, Yuhlong Lio, Sanku Dey
Summary: This paper investigates the inference for the Matusita measure between independent Generalized Inverted Exponential Distributions (GIEDs) under progressive first-failure censoring. The maximum likelihood estimator for the Matusita measure is established when the GIEDs have a common scale but different shape parameters, along with the existence and uniqueness of model estimators. An approximate confidence interval and alternative point and interval estimates based on proposed pivotal quantities are constructed. Bootstrap confidence intervals are also provided for comparison. Additionally, likelihood and generalized estimates for the Matusita measure are discussed when the two GIEDs have unequal parameters. Likelihood ratio testing is provided for comparing the equivalence of the interested parameters. Extensive simulation studies are conducted to evaluate the performances of different methods, and two real-life examples are presented for application.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics
Alexey Kudryavtsev, Oleg Shestakov
Summary: The paper discusses the gamma-exponential distribution and the estimation of its parameters, along with the application of logarithmic cumulants method. It also addresses the difficulties associated with the inversion of polygamma functions in concentration parameter estimation.
Article
Statistics & Probability
Kevin Kurt, Rudiger Frey
Summary: In this study, we investigate Markov-modulated affine processes (MMAPs), which are Markov processes created from affine processes by allowing some coefficients to depend on an exogenous Markov process X. MMAPs maintain the tractability of standard affine processes, as their characteristic function has a computationally convenient form. We extend previous work by considering the case where the generator of X is an unbounded operator. We establish the existence of MMAPs using a martingale problem approach, derive the formula for their characteristic function, and examine various mathematical properties.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2022)
Article
Statistics & Probability
Chenhui Zhang, Dehui Wang, Kai Yang, Han Li, Xiaohong Wang
Summary: This paper introduces a new first-order generalized Poisson integer-valued autoregressive process for modeling integer-valued time series with piecewise structure and overdispersion. It discusses basic probabilistic and statistical properties of the model, derives conditional least squares and conditional maximum likelihood estimators, and establishes the asymptotic properties of the estimators. Additionally, two special cases of the process are discussed, and numerical results of the estimates and a real data example are presented.
JOURNAL OF APPLIED STATISTICS
(2022)
Article
Statistics & Probability
Neda Mohammadi, Leonardo Santoro, Victor M. Panaretos
Summary: This study considers the nonparametric estimation of the drift and diffusion coefficients in a Stochastic Differential Equation (SDE) using functional data analysis methods. The proposed estimators relate local parameters to global parameters through a novel Partial Differential Equation (PDE) and do not require any specific functional form assumptions. The study establishes almost sure uniform asymptotic convergence rates for the estimators, taking into account the impact of different sampling frequencies.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2024)
Article
Statistics & Probability
Masafumi Hayashi, Atsushi Takeuchi, Makoto Yamazato
Summary: This article considers subordinators whose Lévy measures are represented as Laplace transforms of measures on (0,infinity), and refers to them as CME-subordinators. The study shows that the transition probabilities of such processes without drifts are absolutely continuous on (0,infinity) with respect to Lebesgue measure. It is also demonstrated that the densities are bounded in space-time and tend to zero as time goes to infinity, with the speed of decrease being closely related to the behavior near the origin of the corresponding Lévy density.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2024)
Article
Statistics & Probability
Huiping Chen, Yong Chen, Yong Liu
Summary: This paper characterizes the relation between the real and complex Wiener-Ito integrals, providing explicit expressions for the kernels of their real and imaginary parts, and obtaining a representation formula for a two-dimensional real Wiener-Ito integral through a finite sum of complex Wiener-Ito integrals. The main tools used are a recursion technique and Malliavin derivative operators. As an application, the regularity of the stationary solution of the stochastic heat equation with dispersion is investigated.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2024)
Article
Statistics & Probability
Clement Foucart, Matija Vidmar
Summary: This study introduces a class of one-dimensional positive Markov processes that generalize continuous-state branching processes by incorporating random collisions. The study establishes that these processes, known as CB processes with collisions (CBCs), are the only Feller processes without negative jumps that satisfy a Laplace duality relationship with one-dimensional diffusions. The study also explores the relationship between CBCs and CB processes with spectrally positive migration, and provides necessary and sufficient conditions for attracting boundaries and the existence of a limiting distribution.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2024)
Article
Statistics & Probability
Jukka Lempa, Ernesto Mordecki, Paavo Salminen
Summary: This paper investigates the characteristics and properties of diffusion spiders and calculates the density of the resolvent kernel. The study of excessive functions leads to the expression of the representing measure for a given excessive function. These results are then applied to solving optimal stopping problems for diffusion spiders.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2024)
Article
Statistics & Probability
Mirko D'Ovidio, Francesco Iafrate
Summary: This article explores the connection between elastic drifted Brownian motions and inverses to tempered subordinators, and establishes a link between multiplicative functionals and dynamical boundary conditions. By representing functionals of the drifted Brownian motion as the inverse of a tempered subordinator, the problem is simplified.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2024)
Article
Statistics & Probability
M. Heldman, S. A. Isaacson, J. Ma, K. Spiliopoulos
Summary: This study derives and proves the large-population mean-field limit for particle-based stochastic reaction-diffusion models, and provides the next order fluctuation corrections. Numerical examples demonstrate the importance of fluctuation corrections for accurate estimation of higher order statistics in the underlying model.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2024)
Article
Statistics & Probability
Renan Gross
Summary: This study focuses on the problem of scenery reconstruction on d-dimensional torus. The researchers proved that the criterion on Fourier coefficients for discrete cycles, discovered by Matzinger and Lember in 2006, also applies in continuous spaces. It is shown that with the right drift, Brownian motion can be used to reconstruct any scenery. The injectivity property of an infinite Vandermonde matrix is also proven.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2024)
