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Alea-Latin American Journal of Probability and Mathematical Statistics最新文献

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On SDEs for Bessel Processes in low dimension and path-dependent extensions 低维贝塞尔过程的SDEs和路径相关扩展
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2022-11-09 DOI: 10.30757/alea.v20-41
A. Ohashi, Francesco G. Russo, Alan Teixeira
{"title":"On SDEs for Bessel Processes in low dimension and path-dependent extensions","authors":"A. Ohashi, Francesco G. Russo, Alan Teixeira","doi":"10.30757/alea.v20-41","DOIUrl":"https://doi.org/10.30757/alea.v20-41","url":null,"abstract":"The Bessel process in low dimension (0 $le$ $delta$ $le$ 1) is not an It{^o} process and it is a semimartingale only in the cases $delta$ = 1 and $delta$ = 0. In this paper we first characterize it as the unique solution of an SDE with distributional drift or more precisely its related martingale problem. In a second part, we introduce a suitable notion of path-dependent Bessel processes and we characterize them as solutions of path-dependent SDEs with distributional drift.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48306636","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: 2
Generalized scale functions for spectrally negative Lévy processes 谱负lsamvy过程的广义尺度函数
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2022-09-30 DOI: 10.30757/ALEA.v20-24
J. Contreras, V. Rivero
{"title":"Generalized scale functions for spectrally negative Lévy processes","authors":"J. Contreras, V. Rivero","doi":"10.30757/ALEA.v20-24","DOIUrl":"https://doi.org/10.30757/ALEA.v20-24","url":null,"abstract":"For a spectrally negative L'evy process, scale functions appear in the solution of two-sided exit problems, and in particular in relation with the Laplace transform of the first time it exits a closed interval. In this paper, we consider the Laplace transform of more general functionals, which can depend simultaneously on the values of the process and its supremum up to the exit time. These quantities will be expressed in terms of generalized scale functions, which can be defined using excursion theory. In the case the functional does not depend on the supremum, these scale functions coincide with the ones found on the literature, and therefore the results in this work are an extension of them.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45147807","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
Existence of quasi-stationary distributions for spectrally positive Lévy processes on the half-line 半直线上谱正Lévy过程的拟平稳分布的存在性
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2022-08-24 DOI: 10.30757/alea.v20-23
Kosuke Yamato
{"title":"Existence of quasi-stationary distributions for spectrally positive Lévy processes on the half-line","authors":"Kosuke Yamato","doi":"10.30757/alea.v20-23","DOIUrl":"https://doi.org/10.30757/alea.v20-23","url":null,"abstract":"For spectrally positive L'evy processes killed on exiting the half-line, existence of a quasi-stationary distribution is characterized by the exponential integrability of the exit time, the Laplace exponent and the non-negativity of the scale functions. It is proven that if there is a quasi-stationary distribution, there are necessarily infinitely many ones and the set of quasi-stationary distributions is characterized. A sufficient condition for the minimal quasi-stationary distribution to be the Yaglom limit is given.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49547453","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: 4
A note on 3d-monochromatic random waves and cancellation 关于三维单色随机波及其消除的一点注记
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2022-08-22 DOI: 10.30757/alea.v20-40
F. Dalmao
{"title":"A note on 3d-monochromatic random waves and cancellation","authors":"F. Dalmao","doi":"10.30757/alea.v20-40","DOIUrl":"https://doi.org/10.30757/alea.v20-40","url":null,"abstract":"In this note we prove that the asymptotic variance of the nodal length of complex-valued monochromatic random waves restricted to an increasing domain in $R^3$ is linear in the volume of the domain. Put together with previous results this shows that a Central Limit Theorem holds true for $3$-dimensional monochromatic random waves. We compare with the variance of the nodal length of the real-valued $2$-dimensional monochromatic random waves where a faster divergence rate is observed, this fact is connected with Berry's cancellation phenomenon. Moreover, we show that a concentration phenomenon takes place.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49619858","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
Recurrence and transience of Rademacher series Rademacher级数的递归性与短暂性
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2022-05-30 DOI: 10.30757/alea.v20-03
Satyaki Bhattacharya, S. Volkov
{"title":"Recurrence and transience of Rademacher series","authors":"Satyaki Bhattacharya, S. Volkov","doi":"10.30757/alea.v20-03","DOIUrl":"https://doi.org/10.30757/alea.v20-03","url":null,"abstract":"We introduce the notion of {bf a}-walk $S(n)=a_1 X_1+dots+a_n X_n$, based on a sequence of positive numbers ${bf a}=(a_1,a_2,dots)$ and a Rademacher sequence $X_1,X_2,dots$. We study recurrence/transience (properly defined) of such walks for various sequences of ${bf a}$. In particular, we establish the classification in the cases where $a_k=lfloor k^betarfloor$, $beta>0$, as well as in the case $a_k=lceil log_gamma k rceil$ or $a_k=log_gamma k$ for $gamma>1$.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43255046","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
XX^T matrices with independent entries 有独立元素的XX^T矩阵
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2022-05-22 DOI: 10.30757/alea.v20-05
A. Bose, Priyanka Sen
{"title":"XX^T matrices with independent entries","authors":"A. Bose, Priyanka Sen","doi":"10.30757/alea.v20-05","DOIUrl":"https://doi.org/10.30757/alea.v20-05","url":null,"abstract":"Let $S=XX^T$ be the (unscaled) sample covariance matrix where $X$ is a real $p times n$ matrix with independent entries. It is well known that if the entries of $X$ are independent and identically distributed (i.i.d.) with enough moments and $p/n to yneq 0$, then the limiting spectral distribution (LSD) of $frac{1}{n}S$ converges to a Mar$check{text{c}}$enko-Pastur law. Several extensions of this result are also known. We prove a general result on the existence of the LSD of $S$ in probability or almost surely, and in particular, many of the above results follow as special cases. At the same time several new LSD results also follow from our general result. The moments of the LSD are quite involved but can be described via a set of partitions. Unlike in the i.i.d. entries case, these partitions are not necessarily non-crossing, but are related to the special symmetric partitions which are known to appear in the LSD of (generalised) Wigner matrices with independent entries. We also investigate the existence of the LSD of $S_{A}=AA^T$ when $A$ is the $ptimes n$ symmetric or the asymmetric version of any of the following four random matrices: reverse circulant, circulant, Toeplitz and Hankel. The LSD of $frac{1}{n}S_{A}$ for the above four cases have been studied by Bose, Gangopadhyay and Sen in 2010, when the entries are i.i.d. We show that under some general assumptions on the entries of $A$, the LSD of $S_{A}$ exists and this result generalises the existing results significantly.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45943447","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: 2
An evolution model with uncountably many alleles 具有无数等位基因的进化模型
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2022-04-30 DOI: 10.30757/alea.v20-38
D. Bertacchi, J. Lember, F. Zucca
{"title":"An evolution model with uncountably many alleles","authors":"D. Bertacchi, J. Lember, F. Zucca","doi":"10.30757/alea.v20-38","DOIUrl":"https://doi.org/10.30757/alea.v20-38","url":null,"abstract":"We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are characterized by their genome, picked inside a set $X$ (which may be uncountable), and there is a fitness associated to each genome. Being less fit implies a higher chance of being discarded in the selection process. The stationary distribution of the process can be described and studied. We are interested in the asymptotic behavior of this stationary distribution as $n$ goes to infinity. Choosing a parameter $lambda>0$ to tune the scaling of the fitness when $n$ grows, we prove limiting theorems both for the case when the breeding process does not depend on $n$, and for the case when it is given by a Dirichlet process prior. In both cases, the limit exhibits phase transitions depending on the parameter $lambda","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48819146","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
Balls-in-bins models with asymmetric feedback and reflection 具有非对称反馈和反射的弹壳模型
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2022-04-12 DOI: 10.30757/alea.v20-01
M. Menshikov, V. Shcherbakov
{"title":"Balls-in-bins models with asymmetric feedback and reflection","authors":"M. Menshikov, V. Shcherbakov","doi":"10.30757/alea.v20-01","DOIUrl":"https://doi.org/10.30757/alea.v20-01","url":null,"abstract":"Balls-in-bins models describe a random sequential allocation of infinitely many balls into a finite number of bins. In these models a ball is placed into a bin with probability proportional to a given function (feedback function), which depends on the number of existing balls in the bin. Typically, the feedback function is the same for all bins (symmetric feedback), and there are no constraints on the number of balls in the bins. In this paper we study versions of BB models with two bins, in which the above assumptions are violated. In the first model of interest the feedback functions can depend on a bin (BB model with asymmetric feedback). In the case when both feedback functions are power law and superlinear, a single bin receives all but finitely many balls almost surely, and we study the probability that this happens for a given bin. In particular, under certain initial conditions we derive the normal approximation for this probability, which generalizes the result in [5] obtained in the case of the symmetric feedback. The main part of the paper concerns the BB model with asymmetric feedback evolving subject to certain constraints on the numbers of allocated balls. The model can be interpreted as a transient reflecting random walk in a curvilinear wedge, and we obtain a complete classification of its long term behavior.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43559317","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
Dynamical large deviations for the boundary driven symmetric exclusion process with Robin boundary conditions 具有Robin边界条件的边界驱动对称不相容过程的动力学大偏差
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2022-03-27 DOI: 10.30757/alea.v19-60
T. Franco, P. Gonccalves, C. Landim, A. Neumann
{"title":"Dynamical large deviations for the boundary driven symmetric exclusion process with Robin boundary conditions","authors":"T. Franco, P. Gonccalves, C. Landim, A. Neumann","doi":"10.30757/alea.v19-60","DOIUrl":"https://doi.org/10.30757/alea.v19-60","url":null,"abstract":". In this article, we consider a one-dimensional symmetric exclusion process in weak contact with reservoirs at the boundary. In the diffusive time-scaling the empirical measure evolves according to the heat equation with Robin boundary conditions. We prove the associated dynamical large deviations principle.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47231980","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
Slow, ordinary and rapid points for Gaussian Wavelets Series and application to Fractional Brownian Motions 高斯小波级数的慢、常、快点及其在分数布朗运动中的应用
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2022-03-10 DOI: 10.30757/alea.v19-59
C. Esser, L. Loosveldt
{"title":"Slow, ordinary and rapid points for Gaussian Wavelets Series and application to Fractional Brownian Motions","authors":"C. Esser, L. Loosveldt","doi":"10.30757/alea.v19-59","DOIUrl":"https://doi.org/10.30757/alea.v19-59","url":null,"abstract":". We study the Hölderian regularity of Gaussian wavelets series and show that they dis-play, almost surely, three types of points: slow, ordinary and rapid. In particular, this fact holds for the Fractional Brownian Motion. Finally, we remark that the existence of slow points is specific to these functions.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48363925","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: 7
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