{"title":"The First-Passage Area of Wiener Process withStochastic Resetting","authors":"Mario Abundo","doi":"10.1007/s11009-023-10069-4","DOIUrl":"https://doi.org/10.1007/s11009-023-10069-4","url":null,"abstract":"<p>For a one-dimensional Wiener process with stochastic resetting <span>(mathcal{X}(t))</span>, obtained from an underlying Wiener process <i>X</i>(<i>t</i>), we study the statistical properties of its first-passage time through zero, when starting from <span>(X>0,)</span> and its first-passage area, that is the random area enclosed between the time axis and the path of the process <span>(mathcal{X} (t))</span> up to the first-passage time through zero. By making use of solutions of certain associated ODEs, we are able to find explicit expressions for the Laplace transforms of the first-passage time and the first-passage area, and their single and joint moments.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138531337","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}
Jyy-I Hong, Joseph Najnudel, Siang-Mao Rao, Ju-Yi Yen
{"title":"Random Apportionment: A Stochastic Solution to the Balinski-Young Impossibility","authors":"Jyy-I Hong, Joseph Najnudel, Siang-Mao Rao, Ju-Yi Yen","doi":"10.1007/s11009-023-10070-x","DOIUrl":"https://doi.org/10.1007/s11009-023-10070-x","url":null,"abstract":"<p>An apportionment paradox occurs when the rules for apportionment in a political system or distribution system produce results which seem to violate common sense. For example, The Alabama paradox occurs when the total number of seats increases but decreases the allocated number of a state and the population paradox occurs when the population of a state increases but its allocated number of seats decreases. The Balinski-Young impossibility theorem showed that there is no deterministic apportionment method that can avoid the violation of the quota rule and doesn’t have both the Alabama and the population paradoxes. In this paper, we propose a randomized apportionment method as a stochastic solution to the Balinski-Young impossibility.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138531340","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":"Distribution of Patterns of Constrained Length in Binary Sequences","authors":"Frosso S. Makri, Zaharias M. Psillakis","doi":"10.1007/s11009-023-10068-5","DOIUrl":"https://doi.org/10.1007/s11009-023-10068-5","url":null,"abstract":"<p>On a finite sequence of binary (0-1) trials we define a random variable enumerating patterns of length subject to certain constraints. For sequences of independent and identically distributed binary trials exact probability mass functions are established in closed forms by means of combinatorial analysis. An explicit expression of the mean value of this random variable is obtained. The results associated with the probability mass functions are extended on sequences of exchangeable binary trials. An application in Information theory concerning counting of a class of run-length-limited binary sequences is provided as a direct byproduct of our study. Illustrative numerical examples exemplify further the results.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138531333","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":"Equilibrium Queueing Strategies in M/G/1 Queues with the Reference Time Effect","authors":"Tao Jiang, Li Gao, Xudong Chai","doi":"10.1007/s11009-023-10062-x","DOIUrl":"https://doi.org/10.1007/s11009-023-10062-x","url":null,"abstract":"<p>Waiting is a major factor influencing the perception of delay-sensitive customers in the service industry. In the process of queueing, some customers often have a psychological expectation of waiting time in the face of uncertain delay information, so that customer service utility depends not only on the actual waiting time, but also on the relative amount of the actual waiting time and the psychological expectation of waiting time. Therefore, this paper investigates how the reference time effect affects heterogeneous customers' queueing decisions and service system efficiency measures (system throughput and social welfare) in an M/G/1 queue with limited service resources and capacity. The results show that the equilibrium joining probability of customers, the system throughput and social welfare are relatively higher as the proportion of customers with high tolerance levels in the queue increases. In addition, the maintenance of customer homogeneity is better for the improvement of service resource utilization, while the maintenance of customer heterogeneity is better for social welfare. As the psychological expected waiting time increases, the equilibrium joining probability of potential customers and the system throughput increase, while the equilibrium joining probability of existing customers decreases, and the social welfare shows a non-monotonic trend of first decreasing and then increasing. The equilibrium queueing strategies for each type of customer and the service system efficiency measures are not monotonic with the change of the reference time effect parameter. Finally, the optimal social welfare is increasing with respect to the degree of reference time effect and the psychological expectation of waiting time.</p>","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138531336","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":"Asymptotics of Sum of Heavy-tailed Risks with Copulas","authors":"Fan Yang, Yi Zhang","doi":"10.1007/s11009-023-10066-7","DOIUrl":"https://doi.org/10.1007/s11009-023-10066-7","url":null,"abstract":"","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136348597","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":"Ruin Problems for Risk Processes with Dependent Phase-Type Claims","authors":"Oscar Peralta, Matthieu Simon","doi":"10.1007/s11009-023-10065-8","DOIUrl":"https://doi.org/10.1007/s11009-023-10065-8","url":null,"abstract":"","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135431078","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":"A Semi-Markov Model with Geometric Renewal Processes","authors":"Jingqi Zhang, Mitra Fouladirad, Nikolaos Limnios","doi":"10.1007/s11009-023-10060-z","DOIUrl":"https://doi.org/10.1007/s11009-023-10060-z","url":null,"abstract":"","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135774380","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":"Three Distributions in the Extended Occupancy Problem","authors":"Ben O’Neill","doi":"10.1007/s11009-023-10053-y","DOIUrl":"https://doi.org/10.1007/s11009-023-10053-y","url":null,"abstract":"Abstract The classical and extended occupancy distributions are useful for examining the number of occupied bins in problems involving random allocation of balls to bins. We examine the extended occupancy problem by framing it as a Markov chain and deriving the spectral decomposition of the transition probability matrix. We look at three distributions of interest that arise from the problem, all involving the noncentral Stirling numbers of the second kind. These distributions give a useful generalisation to the binomial and negative-binomial distributions. We examine how these distributions relate to one another, and we derive recursive properties and mixture properties that characterise the distributions.","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136102436","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}
Paul A. Jenkins, Murray Pollock, Gareth O. Roberts
{"title":"Flexible Bayesian Inference for Diffusion Processesusing Splines","authors":"Paul A. Jenkins, Murray Pollock, Gareth O. Roberts","doi":"10.1007/s11009-023-10056-9","DOIUrl":"https://doi.org/10.1007/s11009-023-10056-9","url":null,"abstract":"Abstract We introduce a flexible method to simultaneously infer both the drift and volatility functions of a discretely observed scalar diffusion. We introduce spline bases to represent these functions and develop a Markov chain Monte Carlo algorithm to infer, a posteriori, the coefficients of these functions in the spline basis. A key innovation is that we use spline bases to model transformed versions of the drift and volatility functions rather than the functions themselves. The output of the algorithm is a posterior sample of plausible drift and volatility functions that are not constrained to any particular parametric family. The flexibility of this approach provides practitioners a powerful investigative tool, allowing them to posit a variety of parametric models to better capture the underlying dynamics of their processes of interest. We illustrate the versatility of our method by applying it to challenging datasets from finance, paleoclimatology, and astrophysics. In view of the parametric diffusion models widely employed in the literature for those examples, some of our results are surprising since they call into question some aspects of these models.","PeriodicalId":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136262695","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}