Journal of Applied Probability最新文献

{"title":"Sharp large deviations and concentration inequalities for the number of descents in a random permutation","authors":"Bernard Bercu, Michel Bonnefont, Adrien Richou","doi":"10.1017/jpr.2023.86","DOIUrl":"https://doi.org/10.1017/jpr.2023.86","url":null,"abstract":"<p>The goal of this paper is to go further in the analysis of the behavior of the number of descents in a random permutation. Via two different approaches relying on a suitable martingale decomposition or on the Irwin–Hall distribution, we prove that the number of descents satisfies a sharp large-deviation principle. A very precise concentration inequality involving the rate function in the large-deviation principle is also provided.</p>","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"25 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139103556","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}

{"title":"On the Kolmogorov constant explicit form in the theory of discrete-time stochastic branching systems","authors":"Azam A. Imomov, Misliddin S. Murtazaev","doi":"10.1017/jpr.2023.85","DOIUrl":"https://doi.org/10.1017/jpr.2023.85","url":null,"abstract":"<p>We consider a discrete-time population growth system called the Bienaymé–Galton–Watson stochastic branching system. We deal with a noncritical case, in which the per capita offspring mean <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240103141917319-0909:S0021900223000852:S0021900223000852_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$mneq1$</span></span></img></span></span>. The famous Kolmogorov theorem asserts that the expectation of the population size in the subcritical case <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240103141917319-0909:S0021900223000852:S0021900223000852_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$m&lt;1$</span></span></img></span></span> on positive trajectories of the system asymptotically stabilizes and approaches <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240103141917319-0909:S0021900223000852:S0021900223000852_inline3.png\"><span data-mathjax-type=\"texmath\"><span>${1}/mathcal{K}$</span></span></img></span></span>, where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240103141917319-0909:S0021900223000852:S0021900223000852_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal{K}$</span></span></img></span></span> is called the Kolmogorov constant. The paper is devoted to the search for an explicit expression of this constant depending on the structural parameters of the system. Our argumentation is essentially based on the basic lemma describing the asymptotic expansion of the probability-generating function of the number of individuals. We state this lemma for the noncritical case. Subsequently, we find an extended analogue of the Kolmogorov constant in the noncritical case. An important role in our discussion is also played by the asymptotic properties of transition probabilities of the Q-process and their convergence to invariant measures. Obtaining the explicit form of the extended Kolmogorov constant, we refine several limit theorems of the theory of noncritical branching systems, showing explicit leading terms in the asymptotic expansions.</p>","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"35 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139095364","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}

{"title":"Weak convergence of the extremes of branching Lévy processes with regularly varying tails","authors":"Yan-xia Ren, Renming Song, Rui Zhang","doi":"10.1017/jpr.2023.103","DOIUrl":"https://doi.org/10.1017/jpr.2023.103","url":null,"abstract":"We study the weak convergence of the extremes of supercritical branching Lévy processes <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900223001031_inline1.png\" /> <jats:tex-math> ${mathbb{X}_t, t ge0}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> whose spatial motions are Lévy processes with regularly varying tails. The result is drastically different from the case of branching Brownian motions. We prove that, when properly renormalized, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900223001031_inline2.png\" /> <jats:tex-math> $mathbb{X}_t$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> converges weakly. As a consequence, we obtain a limit theorem for the order statistics of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900223001031_inline3.png\" /> <jats:tex-math> $mathbb{X}_t$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"11 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524156","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}

{"title":"Speed of extinction for continuous-state branching processes in a weakly subcritical Lévy environment","authors":"Natalia Cardona-Tobón, Juan Carlos Pardo","doi":"10.1017/jpr.2023.92","DOIUrl":"https://doi.org/10.1017/jpr.2023.92","url":null,"abstract":"We continue with the systematic study of the speed of extinction of continuous-state branching processes in Lévy environments under more general branching mechanisms. Here, we deal with the weakly subcritical regime under the assumption that the branching mechanism is regularly varying. We extend recent results of Li and Xu (2018) and Palau et al. (2016), where it is assumed that the branching mechanism is stable, and complement the recent articles of Bansaye et al. (2021) and Cardona-Tobón and Pardo (2021), where the critical and the strongly and intermediate subcritical cases were treated, respectively. Our methodology combines a path analysis of the branching process together with its Lévy environment, fluctuation theory for Lévy processes, and the asymptotic behaviour of exponential functionals of Lévy processes. Our approach is inspired by the last two previously cited papers, and by Afanasyev et al. (2012), where the analogue was obtained.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"24 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524155","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}

{"title":"JPR volume 60 issue 4 Cover and Front matter","authors":"","doi":"10.1017/jpr.2023.55","DOIUrl":"https://doi.org/10.1017/jpr.2023.55","url":null,"abstract":"","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"121 2","pages":"f1 - f2"},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139012773","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}

{"title":"JPR volume 60 issue 4 Cover and Back matter","authors":"","doi":"10.1017/jpr.2023.56","DOIUrl":"https://doi.org/10.1017/jpr.2023.56","url":null,"abstract":"","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"124 ","pages":"b1 - b2"},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138988690","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}

{"title":"Daryl John Daley, 4 April 1939 – 16 April 2023 An internationally acclaimed researcher in applied probability and a gentleman of great kindness","authors":"Peter G. Taylor","doi":"10.1017/jpr.2023.90","DOIUrl":"https://doi.org/10.1017/jpr.2023.90","url":null,"abstract":"","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"271 2","pages":"1516 - 1531"},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139022048","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}

{"title":"Local convergence of critical Galton–Watson trees","authors":"Aymen Bouaziz","doi":"10.1017/jpr.2023.83","DOIUrl":"https://doi.org/10.1017/jpr.2023.83","url":null,"abstract":"We study the local convergence of critical Galton–Watson trees under various conditionings. We give a sufficient condition, which serves to cover all previous known results, for the convergence in distribution of a conditioned Galton–Watson tree to Kesten’s tree. We also propose a new proof to give the limit in distribution of a critical Galton–Watson tree, with finite support, conditioned on having a large width.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"27 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524152","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}

{"title":"Dynamics of information networks","authors":"Andrei Sontag, Tim Rogers, Christian A Yates","doi":"10.1017/jpr.2023.91","DOIUrl":"https://doi.org/10.1017/jpr.2023.91","url":null,"abstract":"We explore a simple model of network dynamics which has previously been applied to the study of information flow in the context of epidemic spreading. A random rooted network is constructed that evolves according to the following rule: at a constant rate, pairs of nodes (<jats:italic>i</jats:italic>, <jats:italic>j</jats:italic>) are randomly chosen to interact, with an edge drawn from <jats:italic>i</jats:italic> to <jats:italic>j</jats:italic> (and any other out-edge from <jats:italic>i</jats:italic> deleted) if <jats:italic>j</jats:italic> is strictly closer to the root with respect to graph distance. We characterise the dynamics of this random network in the limit of large size, showing that it instantaneously forms a tree with long branches that immediately collapse to depth two, then it slowly rearranges itself to a star-like configuration. This curious behaviour has consequences for the study of the epidemic models in which this information network was first proposed.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"47 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524207","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}

{"title":"Characteristics of the switch process and geometric divisibility","authors":"Henrik Bengtsson","doi":"10.1017/jpr.2023.81","DOIUrl":"https://doi.org/10.1017/jpr.2023.81","url":null,"abstract":"Abstract The switch process alternates independently between 1 and $-1$ , with the first switch to 1 occurring at the origin. The expected value function of this process is defined uniquely by the distribution of switching times. The relation between the two is implicitly described through the Laplace transform, which is difficult to use for determining if a given function is the expected value function of some switch process. We derive an explicit relation under the assumption of monotonicity of the expected value function. It is shown that geometric divisible switching time distributions correspond to a non-negative decreasing expected value function. Moreover, an explicit relation between the expected value of a switch process and the autocovariance function of the switch process stationary counterpart is obtained, leading to a new interpretation of the classical Pólya criterion for positive-definiteness.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135635344","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}