Stochastic Analysis and Applications最新文献

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Mixed Poisson process with Stacy mixing variable 具有Stacy混合变量的混合泊松过程

IF 1.3 4区数学 Q2 Mathematics

Stochastic Analysis and Applications

Pub Date : 2023-03-17 DOI: 10.1080/07362994.2023.2242471

P. Jordanova, Mladen Savov, Assen Tchorbadjieff, Milan Stehl'ik

Stacy distribution defined for the first time in 1961 provides a flexible framework for modelling of a wide range of real-life behaviours. It appears under different names in the scientific literature and contains many useful particular cases. Homogeneous Poisson processes are appropriate apriori models for the number of renewals up to a given time $t>0$. This paper mixes them and considers a Mixed Poisson process with Stacy mixing variable. We call it a Poisson-Stacy process. The resulting counting process is one of the Generalised Negative Binomial processes, and the distribution of its time-intersections are very-well investigated in the scientific literature. Here we define and investigate their joint probability distributions. Then, the corresponding mixed renewal process is investigated and Exp-Stacy and Erlang-Stacy distributions are defined and partially studied. The paper finishes with a simulation study of these stochastic processes. Some plots of the probability density functions, probability mass functions, mean square regressions and sample paths are drawn together with the corresponding code for the simulations.

1961年首次定义的史黛西分布为广泛的现实生活行为建模提供了一个灵活的框架。它在科学文献中以不同的名称出现，并包含许多有用的特殊案例。齐次泊松过程是适用于给定时间内更新次数的先验模型。本文将它们混合在一起，考虑了一个具有Stacy混合变量的混合泊松过程。我们称之为泊松-史黛西过程。由此产生的计数过程是广义负二项过程之一，其时间交叉点的分布在科学文献中得到了很好的研究。这里我们定义并研究它们的联合概率分布。然后，研究了相应的混合更新过程，定义了Exp-Stacy和Erlang-Stacy分布，并对其进行了部分研究。本文最后对这些随机过程进行了模拟研究。绘制了概率密度函数图、概率质量函数图、均方回归图和样本路径图，并给出了相应的仿真代码。

引用次数: 0

On dose-response modeling for evaluation of drugs combinations 评价药物组合的剂量-反应模型

IF 1.3 4区数学 Q2 Mathematics

Stochastic Analysis and Applications

Pub Date : 2023-02-01 DOI: 10.1080/07362994.2023.2170885

N. Flournoy, L. Hearne, J. Kiseľák, M. Stehlík

引用次数: 0

On stochastic aspects of impact modeling of the innovation incentive system and business internationalization: evidence from Portuguese SMEs 创新激励制度与企业国际化影响模型的随机方面:来自葡萄牙中小企业的证据

IF 1.3 4区数学 Q2 Mathematics

Stochastic Analysis and Applications

Pub Date : 2023-01-17 DOI: 10.1080/07362994.2023.2166532

L. Grilo, E. J. Pereira, J. P. Maidana, M. Stehlík

引用次数: 1

Stochastic approach to heterogeneity in short-time announcement effects on the Chilean stock market indexes within 2016-2019 2016-2019年短期公告对智利股市指数影响异质性的随机方法

IF 1.3 4区数学 Q2 Mathematics

Stochastic Analysis and Applications

Pub Date : 2023-01-16 DOI: 10.1080/07362994.2022.2164508

M. Stehlík, Danilo Leal, J. Kiseľák, Joshua Leers, L. Střelec, F. Fuders

引用次数: 1

A Lyapunov approach to stability of positive semigroups: an overview with illustrations 正半群稳定性的Lyapunov方法:附插图的概述

IF 1.3 4区数学 Q2 Mathematics

Stochastic Analysis and Applications

Pub Date : 2023-01-09 DOI: 10.1080/07362994.2023.2206880

M. Arnaudon, P. Moral, E. Ouhabaz

The stability analysis of possibly time varying positive semigroups on non necessarily compact state spaces, including Neumann and Dirichlet boundary conditions is a notoriously difficult subject. These crucial questions arise in a variety of areas of applied mathematics, including nonlinear filtering, rare event analysis, branching processes, physics and molecular chemistry. This article presents an overview of some recent Lyapunov-based approaches, focusing principally on practical and powerful tools for designing Lyapunov functions. These techniques include semigroup comparisons as well as conjugacy principles on non necessarily bounded manifolds with locally Lipschitz boundaries. All the Lyapunov methodologies discussed in the article are illustrated in a variety of situations, ranging from conventional Markov semigroups on general state spaces to more sophisticated conditional stochastic processes possibly restricted to some non necessarily bounded domains, including locally Lipschitz and smooth hypersurface boundaries, Langevin diffusions as well as coupled harmonic oscillators.

非必然紧态空间上可能时变正半群的稳定性分析是一个非常困难的问题，包括Neumann和Dirichlet边界条件。这些关键问题出现在应用数学的各个领域，包括非线性滤波、罕见事件分析、分支过程、物理和分子化学。本文概述了一些最近的基于李雅普诺夫的方法，主要侧重于设计李雅普诺夫函数的实用和强大的工具。这些技术包括半群比较以及具有局部Lipschitz边界的非必然有界流形的共轭原理。文章中讨论的所有Lyapunov方法都在各种情况下进行了说明，从一般状态空间上的传统马尔可夫半群到更复杂的条件随机过程，这些过程可能限制在一些非必然有界的域中，包括局部Lipschitz和光滑超表面边界，Langevin扩散以及耦合谐振子。

引用次数: 1

Forward-backward stochastic equations: a functional fixed point approach 前后向随机方程组：一种函数不动点方法

IF 1.3 4区数学 Q2 Mathematics

Stochastic Analysis and Applications

Pub Date : 2023-01-02 DOI: 10.1080/07362994.2021.1988857

Kihun Nam, Yunxi Xu

Abstract We introduce forward-backward stochastic equations (FBSEs) that incorporate fully-coupled forward-backward structure into backward stochastic equations (BSEs) introduced in Cheridito and Nam (Ann. Probab. 45(6A):3795–3828, 2017). Such a system generalizes the classical backward stochastic differential equations (BSDEs) and forward-backward stochastic differential equations (FBSDEs) in previous literature. We transform an FBSE into a fixed point equation on the space of random variables and then apply general fixed point theorems to derive the existence and/or uniqueness of a solution. As a result, we obtain novel existence and/or uniqueness results for fully-coupled FBSDEs with functional drivers, which are either Lipschitz or non-Lipschitz.

摘要：我们引入了前向-后向随机方程（FBSE），该方程将完全耦合的前向-向后结构纳入Cheridito和Nam（Ann.Prob.45（6A）:3795–38282017）中引入的向后随机方程（BSE）中。该系统推广了以往文献中的经典后向随机微分方程（BSDE）和前向后向随机方程（FBSDE）。我们将FBSE转化为随机变量空间上的不动点方程，然后应用一般的不动点定理来导出解的存在性和/或唯一性。因此，我们获得了具有功能驱动器的完全耦合FBSDE的新的存在性和/或唯一性结果，这些驱动器是Lipschitz或非Lipschitz。

引用次数: 1

REDACS: Regional emergency-driven adaptive cluster sampling for effective COVID-19 management. REDACS:针对COVID-19有效管理的区域应急驱动自适应整群抽样

IF 1.3 4区数学 Q2 Mathematics

Stochastic Analysis and Applications

Pub Date : 2023-01-01 Epub Date: 2022-02-25 DOI: 10.1080/07362994.2022.2033126

M Stehlík, J Kisel'ák, A Dinamarca, E Alvarado, F Plaza, F A Medina, S Stehlíková, J Marek, B Venegas, A Gajdoš, Y Li, S Katuščák, A Bražinová, E Zeintl, Y Lu

As COVID-19 is spreading, national agencies need to monitor and track several metrics. Since we do not have perfect testing programs on the hand, one needs to develop an advanced sampling strategies for prevalence study, control and management. Here we introduce REDACS: Regional emergency-driven adaptive cluster sampling for effective COVID-19 management and control and justify its usage for COVID-19. We show its advantages over classical massive individual testing sampling plans. We also point out how regional and spatial heterogeneity underlines proper sampling. Fundamental importance of adaptive control parameters from emergency health stations and medical frontline is outlined. Since the Northern hemisphere entered Autumn and Winter season (this paper was originally submitted in November 2020), practical illustration from spatial heterogeneity of Chile (Southern hemisphere, which already experienced COVID-19 winter outbreak peak) is underlying the importance of proper regional heterogeneity of sampling plan. We explain the regional heterogeneity by microbiological backgrounds and link it to behavior of Lyapunov exponents. We also discuss screening by antigen tests from the perspective of "on the fly" biomarker validation, i.e., during the screening.

摘要随着新冠肺炎的传播，国家机构需要监测和跟踪几个指标。由于我们手头没有完善的检测计划，因此需要制定先进的抽样策略来进行流行率研究、控制和管理。在此，我们介绍REDACS：区域应急驱动的自适应集群采样，用于有效的新冠肺炎管理和控制，并证明其在新冠肺炎中的应用。我们展示了它相对于经典的大规模个体测试抽样计划的优势。我们还指出了区域和空间异质性如何强调适当的采样。概述了来自急救站和医疗一线的自适应控制参数的基本重要性。自北半球进入秋冬季节（本文最初提交于2020年11月）以来，智利（南半球，已经经历了新冠肺炎冬季爆发高峰）的空间异质性的实践说明了采样计划的适当区域异质性的重要性。我们通过微生物背景来解释区域异质性，并将其与李雅普诺夫指数的行为联系起来。我们还从“动态”生物标志物验证的角度讨论了抗原测试的筛选，即在筛选过程中。

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引用次数: 2

Large deviation principle for a class of stochastic hydrodynamical type systems driven by multiplicative Lévy noises 一类乘性Lévy噪声驱动的随机流体动力学系统的大偏差原理

IF 1.3 4区数学 Q2 Mathematics

Stochastic Analysis and Applications

Pub Date : 2022-12-12 DOI: 10.1080/07362994.2022.2151469

N. T. Da, Lian-bing She

Abstract This article is devoted to the large deviation principle for a wide class of stochastic hydrodynamical systems driven by multiplicative Lévy noise. The model covers many equations arising form fluid dynamics such as 2D Navier-Stokes equations, 2D MHD models and the 2D magnetic Bénard problem and also shell models of turbulence. The main difficulty in proving the large deviation principle for the system is overcame by using the weak convergence method introduced by Budhiraja, Dupuis and Maroulas (Ann. Probab. 36: 1390–1420, 2008 and Annales De L Institut Henri Poincare. 47: 725–747, 2011).

引用次数: 0

Ergodicity and approximations of invariant measures for stochastic lattice systems with Markovian switching Markovian切换随机格系统的遍历性和不变测度的逼近

IF 1.3 4区数学 Q2 Mathematics

Stochastic Analysis and Applications

Pub Date : 2022-12-04 DOI: 10.1080/07362994.2022.2144375

Zhang Chen, Xiaoxiao Sun, D. Yang

Abstract This paper is concerned with the dynamics of stochastic lattice systems with Markovian switching. Based on the well-posedness of solutions, we first prove the ergodicity of invariant measures and show that the Markov chain facilitates the existence of invariant measures. In order to investigate numerical invariant measures, the convergence of invariant measures is considered between the original systems and their finite-dimensional truncated systems. Due to this, we can use the backward Euler-Maruyama method to approximate invariant measures for such infinite-dimensional systems. This work provides a feasible path for the convergence of the finite-dimensional numerical invariant measures to the analytical invariant measure.

引用次数: 0

Stochastic inclusions and set-valued stochastic equations with mixed integrals in the plane 平面上具有混合积分的随机包涵和集值随机方程

IF 1.3 4区数学 Q2 Mathematics

Stochastic Analysis and Applications

Pub Date : 2022-11-26 DOI: 10.1080/07362994.2022.2144890

M. Michta

Abstract The paper refers to the study of properties of solutions to two-parameter stochastic inclusions and set-valued stochastic equations with set-valued mixed integrals driven by finite variation processes and martingales. We present new types of such inclusions and equations that generalize those studied earlier. Apart from existence results to such inclusions and equations also topological properties of their solutions are studied. Additionally some connections between their solutions are established. The results obtained in the paper present a set-valued counterpart dealing with this topic known both in deterministic and stochastic cases.

引用次数: 0

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