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Anomalous recurrence of Markov chains on negatively curved manifolds 负弯曲流形上马尔可夫链的反常递推
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2022-10-06 DOI: 10.1017/jpr.2022.40
J. Armstrong, Tim King
{"title":"Anomalous recurrence of Markov chains on negatively curved manifolds","authors":"J. Armstrong, Tim King","doi":"10.1017/jpr.2022.40","DOIUrl":"https://doi.org/10.1017/jpr.2022.40","url":null,"abstract":"Abstract We present a recurrence–transience classification for discrete-time Markov chains on manifolds with negative curvature. Our classification depends only on geometric quantities associated to the increments of the chain, defined via the Riemannian exponential map. We deduce that a recurrent chain that has zero average drift at every point cannot be uniformly elliptic, unlike in the Euclidean case. We also give natural examples of zero-drift recurrent chains on negatively curved manifolds, including on a stochastically incomplete manifold.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"60 1","pages":"204 - 222"},"PeriodicalIF":1.0,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47539275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stationary analysis of an (R, Q) inventory model with normal and emergency orders 具有正常和紧急订单的(R, Q)库存模型的平稳分析
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2022-10-04 DOI: 10.1017/jpr.2022.43
O. Boxma, D. Perry, W. Stadje
{"title":"Stationary analysis of an (R, Q) inventory model with normal and emergency orders","authors":"O. Boxma, D. Perry, W. Stadje","doi":"10.1017/jpr.2022.43","DOIUrl":"https://doi.org/10.1017/jpr.2022.43","url":null,"abstract":"Abstract We consider an (R, Q) inventory model with two types of orders, normal orders and emergency orders, which are issued at different inventory levels. These orders are delivered after exponentially distributed lead times. In between deliveries, the inventory level decreases in a state-dependent way, according to a release rate function \u0000$alpha({cdot})$\u0000 . This function represents the fluid demand rate; it could be controlled by a system manager via price adaptations. We determine the mean number of downcrossings \u0000$theta(x)$\u0000 of any level x in one regenerative cycle, and use it to obtain the steady-state density f (x) of the inventory level. We also derive the rates of occurrence of normal deliveries and of emergency deliveries, and the steady-state probability of having zero inventory.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"60 1","pages":"106 - 126"},"PeriodicalIF":1.0,"publicationDate":"2022-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42508809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The proportion of triangles in a class of anisotropic Poisson line tessellations 一类各向异性泊松线镶嵌中三角形的比例
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2022-09-28 DOI: 10.1017/jpr.2023.45
Nils Heerten, Julia Krecklenberg, Christoph Thale
{"title":"The proportion of triangles in a class of anisotropic Poisson line tessellations","authors":"Nils Heerten, Julia Krecklenberg, Christoph Thale","doi":"10.1017/jpr.2023.45","DOIUrl":"https://doi.org/10.1017/jpr.2023.45","url":null,"abstract":"\u0000 Stationary Poisson processes of lines in the plane are studied, whose directional distributions are concentrated on \u0000 \u0000 \u0000 \u0000$kgeq 3$\u0000\u0000 \u0000 equally spread directions. The random lines of such processes decompose the plane into a collection of random polygons, which form a so-called Poisson line tessellation. The focus of this paper is to determine the proportion of triangles in such tessellations, or equivalently, the probability that the typical cell is a triangle. As a by-product, a new deviation of Miles’s classical result for the isotropic case is obtained by an approximation argument.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44593292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Limit theory for U-statistics under geometric and topological constraints with rare events 具有罕见事件的几何和拓扑约束下u统计量的极限理论
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2022-09-14 DOI: 10.1017/jpr.2022.39
Takashi Owada
{"title":"Limit theory for U-statistics under geometric and topological constraints with rare events","authors":"Takashi Owada","doi":"10.1017/jpr.2022.39","DOIUrl":"https://doi.org/10.1017/jpr.2022.39","url":null,"abstract":"Abstract We study the geometric and topological features of U-statistics of order k when the k-tuples satisfying geometric and topological constraints do not occur frequently. Using appropriate scaling, we establish the convergence of U-statistics in vague topology, while the structure of a non-degenerate limit measure is also revealed. Our general result shows various limit theorems for geometric and topological statistics, including persistent Betti numbers of Čech complexes, the volume of simplices, a functional of the Morse critical points, and values of the min-type distance function. The required vague convergence can be obtained as a result of the limit theorem for point processes induced by U-statistics. The latter convergence particularly occurs in the \u0000$mathcal M_0$\u0000 -topology.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"60 1","pages":"314 - 340"},"PeriodicalIF":1.0,"publicationDate":"2022-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42969664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Extrema of a multinomial assignment process 多项式赋值过程的极值
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2022-09-12 DOI: 10.1017/jpr.2023.26
M. Lifshits, Gilles Mordant
{"title":"Extrema of a multinomial assignment process","authors":"M. Lifshits, Gilles Mordant","doi":"10.1017/jpr.2023.26","DOIUrl":"https://doi.org/10.1017/jpr.2023.26","url":null,"abstract":"\u0000 We study the asymptotic behaviour of the expectation of the maxima and minima of a random assignment process generated by a large matrix with multinomial entries. A variety of results is obtained for different sparsity regimes.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46592988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On connectivity and robustness of random graphs with inhomogeneity 不均匀随机图的连通性和鲁棒性
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2022-09-05 DOI: 10.1017/jpr.2022.32
Y. Shang
{"title":"On connectivity and robustness of random graphs with inhomogeneity","authors":"Y. Shang","doi":"10.1017/jpr.2022.32","DOIUrl":"https://doi.org/10.1017/jpr.2022.32","url":null,"abstract":"Abstract The study of threshold functions has a long history in random graph theory. It is known that the thresholds for minimum degree k, k-connectivity, as well as k-robustness coincide for a binomial random graph. In this paper we consider an inhomogeneous random graph model, which is obtained by including each possible edge independently with an individual probability. Based on an intuitive concept of neighborhood density, we show two sufficient conditions guaranteeing k-connectivity and k-robustness, respectively, which are asymptotically equivalent. Our framework sheds some light on extending uniform threshold values in homogeneous random graphs to threshold landscapes in inhomogeneous random graphs.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"60 1","pages":"284 - 294"},"PeriodicalIF":1.0,"publicationDate":"2022-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49369867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
On the ruin probability of a generalized Cramér–Lundberg model driven by mixed Poisson processes 混合泊松过程驱动下的广义cram<s:1> - lundberg模型的破产概率
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2022-09-01 DOI: 10.1017/jpr.2021.99
Masashi Tomita, Koichiro Takaoka, Motokazu Ishizaka
{"title":"On the ruin probability of a generalized Cramér–Lundberg model driven by mixed Poisson processes","authors":"Masashi Tomita, Koichiro Takaoka, Motokazu Ishizaka","doi":"10.1017/jpr.2021.99","DOIUrl":"https://doi.org/10.1017/jpr.2021.99","url":null,"abstract":"Abstract We propose a generalized Cramér–Lundberg model of the risk theory of non-life insurance and study its ruin probability. Our model is an extension of that of Dubey (1977) to the case of multiple insureds, where the counting process is a mixed Poisson process and the continuously varying premium rate is determined by a Bayesian rule on the number of claims. We use two proofs to show that, for each fixed value of the safety loading, the ruin probability is the same as that of the classical Cramér–Lundberg model and does not depend on either the distribution of the mixing variable of the driving mixed Poisson process or the number of claim contracts.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"59 1","pages":"849 - 859"},"PeriodicalIF":1.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43192292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Coexistence of lazy frogs on ${mathbb{Z}}$ $｛mathbb｛Z｝｝上懒惰青蛙的共存$
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2022-06-28 DOI: 10.1017/jpr.2021.86
Mark Holmes, Daniel Kious
{"title":"Coexistence of lazy frogs on \u0000${mathbb{Z}}$","authors":"Mark Holmes, Daniel Kious","doi":"10.1017/jpr.2021.86","DOIUrl":"https://doi.org/10.1017/jpr.2021.86","url":null,"abstract":"Abstract We study the so-called frog model on \u0000${mathbb{Z}}$\u0000 with two types of lazy frogs, with parameters \u0000$p_1,p_2in (0,1]$\u0000 respectively, and a finite expected number of dormant frogs per site. We show that for any such \u0000$p_1$\u0000 and \u0000$p_2$\u0000 there is positive probability that the two types coexist (i.e. that both types activate infinitely many frogs). This answers a question of Deijfen, Hirscher, and Lopes in dimension one.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"59 1","pages":"702 - 713"},"PeriodicalIF":1.0,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49500521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Discounted optimal stopping problems in first-passage time models with random thresholds 具有随机阈值的首次通过时间模型中的折扣最优停车问题
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2022-06-27 DOI: 10.1017/jpr.2021.85
P. Gapeev, Hessah Al Motairi
{"title":"Discounted optimal stopping problems in first-passage time models with random thresholds","authors":"P. Gapeev, Hessah Al Motairi","doi":"10.1017/jpr.2021.85","DOIUrl":"https://doi.org/10.1017/jpr.2021.85","url":null,"abstract":"Abstract We derive closed-form solutions to some discounted optimal stopping problems related to the perpetual American cancellable dividend-paying put and call option pricing problems in an extension of the Black–Merton–Scholes model. The cancellation times are assumed to occur when the underlying risky asset price process hits some unobservable random thresholds. The optimal stopping times are shown to be the first times at which the asset price reaches stochastic boundaries depending on the current values of its running maximum and minimum processes. The proof is based on the reduction of the original optimal stopping problems to the associated free-boundary problems and the solution of the latter problems by means of the smooth-fit and modified normal-reflection conditions. We show that the optimal stopping boundaries are characterised as the maximal and minimal solutions of certain first-order nonlinear ordinary differential equations.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"59 1","pages":"714 - 733"},"PeriodicalIF":1.0,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43730232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Stopping problems with an unknown state 停止未知状态的问题
IF 1 4区 数学
Journal of Applied Probability Pub Date : 2022-06-22 DOI: 10.1017/jpr.2023.52
Erik Ekström, Yuqiong Wang
{"title":"Stopping problems with an unknown state","authors":"Erik Ekström, Yuqiong Wang","doi":"10.1017/jpr.2023.52","DOIUrl":"https://doi.org/10.1017/jpr.2023.52","url":null,"abstract":"\u0000 We extend the classical setting of an optimal stopping problem under full information to include problems with an unknown state. The framework allows the unknown state to influence (i) the drift of the underlying process, (ii) the payoff functions, and (iii) the distribution of the time horizon. Since the stopper is assumed to observe the underlying process and the random horizon, this is a two-source learning problem. Assigning a prior distribution for the unknown state, standard filtering theory can be employed to embed the problem in a Markovian framework with one additional state variable representing the posterior of the unknown state. We provide a convenient formulation of this Markovian problem, based on a measure change technique that decouples the underlying process from the new state variable. Moreover, we show by means of several novel examples that this reduced formulation can be used to solve problems explicitly.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47024132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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