Alea-Latin American Journal of Probability and Mathematical Statistics最新文献_第10页

Continuity problem for singular BSDE with random terminal time 具有随机终止时间的奇异BSDE的连续性问题

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-11-10 DOI: 10.30757/alea.v19-49

A. Popier, S. Samuel, A. Sezer

{"title":"Continuity problem for singular BSDE with random terminal time","authors":"A. Popier, S. Samuel, A. Sezer","doi":"10.30757/alea.v19-49","DOIUrl":"https://doi.org/10.30757/alea.v19-49","url":null,"abstract":"We study a class of nonlinear BSDEs with a superlinear driver process f adapted to a filtration F and over a random time interval [[0, S]] where S is a stopping time of F. The terminal condition $xi$ is allowed to take the value +$infty$, i.e., singular. Our goal is to show existence of solutions to the BSDE in this setting. We will do so by proving that the minimal supersolution to the BSDE is a solution, i.e., attains the terminal values with probability 1. We consider three types of terminal values: 1) Markovian: i.e., $xi$ is of the form $xi$ = g($Xi$ S) where $Xi$ is a continuous Markovian diffusion process and S is a hitting time of $Xi$ and g is a deterministic function 2) terminal conditions of the form $xi$ = $infty$ $times$ 1 {$tau$ $le$S} and 3) $xi$ 2 = $infty$ $times$ 1 {$tau$ >S} where $tau$ is another stopping time. For general $xi$ we prove the minimal supersolution is continuous at time S provided that F is left continuous at time S. We call a stopping time S solvable with respect to a given BSDE and filtration if the BSDE has a minimal supersolution with terminal value $infty$ at terminal time S. The concept of solvability plays a key role in many of the arguments. Finally, we discuss implications of our results on the Markovian terminal conditions to solution of nonlinear elliptic PDE with singular boundary conditions.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49544036","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 the percolative properties of the intersectionof two independent interlacements 关于两个独立相交点相交的渗透性质

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-10-26 DOI: 10.30757/alea.v18-40

Zijie Zhuang

引用次数: 1

Strict comparison for the Lyapunov exponents of the simple random walk in random potentials 随机势中简单随机游动Lyapunov指数的严格比较

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-10-17 DOI: 10.30757/alea.v20-36

Naoki Kubota

引用次数: 1

Bound on the running maximum of a random walk with small drift 具有小漂移的随机漫步的运行最大值的边界

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-10-17 DOI: 10.30757/alea.v19-03

Ofer Busani, T. Seppalainen

引用次数: 2

On the spectrum and ergodicity of a neutral multi-allelic Moran model 中性多等位基因Moran模型的谱和遍历性

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-10-17 DOI: 10.30757/ALEA.v20-18

J. Corujo

{"title":"On the spectrum and ergodicity of a neutral multi-allelic Moran model","authors":"J. Corujo","doi":"10.30757/ALEA.v20-18","DOIUrl":"https://doi.org/10.30757/ALEA.v20-18","url":null,"abstract":"The purpose of this paper is to provide a complete description of the eigenvalues of the generator of a neutral multi-type Moran model, and the applications to the study of the speed of convergence to stationarity. The Moran model we consider is a non-reversible in general, continuous-time Markov chain with an unknown stationary distribution. Specifically, we consider $N$ individuals such that each one of them is of one type among $K$ possible allelic types. The individuals interact in two ways: by an independent irreducible mutation process and by a reproduction process, where a pair of individuals is randomly chosen, one of them dies and the other reproduces. Our main result provides explicit expressions for the eigenvalues of the infinitesimal generator matrix of the Moran process, in terms of the eigenvalues of the jump rate matrix. As consequences of this result, we study the convergence in total variation of the process to stationarity and show a lower bound for the mixing time of the Moran process. Furthermore, we study in detail the spectral decomposition of the neutral multi-allelic Moran model with parent independent mutation scheme, which is the unique mutation scheme that makes the neutral Moran process reversible. Under the parent independent mutation, we also prove the existence of a cutoff phenomenon in the chi-square and the total variation distances when initially all the individuals are of the same type and the number of individuals tends to infinity. Additionally, in the absence of reproduction, we prove that the total variation distance to stationarity of the parent independent mutation process when initially all the individuals are of the same type has a Gaussian profile.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45652117","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

Where to stand when playing darts? 玩飞镖时该站在哪里?

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-10-01 DOI: 10.30757/alea.v18-57

Björn Franzén, J. Steif, Johan Wastlund

{"title":"Where to stand when playing darts?","authors":"Björn Franzén, J. Steif, Johan Wastlund","doi":"10.30757/alea.v18-57","DOIUrl":"https://doi.org/10.30757/alea.v18-57","url":null,"abstract":"This paper analyzes the question of where one should stand when playing darts. If one stands at distance $d>0$ and aims at $ain mathbb{R}^n$, then the dart (modelled by a random vector $X$ in $mathbb{R}^n$) hits a random point given by $a+dX$. Next, given a payoff function $f$, one considers $$ sup_a Ef(a+dX) $$ and asks if this is decreasing in $d$; i.e., whether it is better to stand closer rather than farther from the target. Perhaps surprisingly, this is not always the case and understanding when this does or does not occur is the purpose of this paper. \u0000We show that if $X$ has a so-called selfdecomposable distribution, then it is always better to stand closer for any payoff function. This class includes all stable distributions as well as many more. \u0000On the other hand, if the payoff function is $cos(x)$, then it is always better to stand closer if and only if the characteristic function $|phi_X(t)|$ is decreasing on $[0,infty)$. We will then show that if there are at least two point masses, then it is not always better to stand closer using $cos(x)$. If there is a single point mass, one can find a different payoff function to obtain this phenomenon. \u0000Another large class of darts $X$ for which there are bounded continuous payoff functions for which it is not always better to stand closer are distributions with compact support. This will be obtained by using the fact that the Fourier transform of such distributions has a zero in the complex plane. This argument will work whenever there is a complex zero of the Fourier transform. \u0000Finally, we analyze if the property of it being better to stand closer is closed under convolution and/or limits.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46412255","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

Truncation of long-range percolation models with square non-summable interactions 具有平方不可和相互作用的远程渗流模型的截断

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-09-28 DOI: 10.30757/alea.v19-41

Alberto M. Campos, B. D. Lima

引用次数: 1

Normal approximation via non-linear exchangeable pairs 通过非线性交换对的正态逼近

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-08-05 DOI: 10.30757/alea.v20-08

C. Dobler

引用次数: 6

A characterization of progressively equivalent probability measures preserving the structure of a compound mixed renewal process 保留化合物混合更新过程结构的渐进等效概率测度的表征

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-07-10 DOI: 10.30757/alea.v20-09

Spyridon M. Tzaninis, N. D. Macheras

引用次数: 2

Large Deviation Principle for the Greedy Exploration Algorithm over Erdös-Rényi Graphs 贪心搜索算法在Erdös-Rényi图上的大偏差原理

IF 0.7 4区数学

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2020-07-09 DOI: 10.30757/alea.v19-16

P. Bermolen, Valeria Goicoechea, M. Jonckheere, E. Mordecki

引用次数: 4