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Dynamic programming approach to reflected backward stochastic differential equations 反映后向随机微分方程的动态规划方法
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp999
Hun O, Mun-Chol Kim, Kon-Gun Kim
{"title":"Dynamic programming approach to reflected backward stochastic differential equations","authors":"Hun O, Mun-Chol Kim, Kon-Gun Kim","doi":"10.1214/23-ejp999","DOIUrl":"https://doi.org/10.1214/23-ejp999","url":null,"abstract":"By introducing a new type of minimality condition, this paper gives a novel approach to the reflected backward stochastic differential equations (RBSDEs) with càdlàg obstacles. Our first step is to prove the dynamic programming principles for nonlinear optimal stopping problems with g-expectations. We then use the nonlinear Doob-Meyer decomposition theorem for g-supermartingales to get the existence of the solution. With a new type of minimality condition, we prove a representation formula of solutions to RBSDEs, in an efficient way. Finally, we derive some a priori estimates and stability results.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136008514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Convergence rate for geometric statistics of point processes having fast decay of dependence 具有快速相关性衰减的点过程几何统计的收敛速度
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp979
Tianshu Cong, A. Xia
{"title":"Convergence rate for geometric statistics of point processes having fast decay of dependence","authors":"Tianshu Cong, A. Xia","doi":"10.1214/23-ejp979","DOIUrl":"https://doi.org/10.1214/23-ejp979","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42439329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Green function estimates for second order elliptic operators in non-divergence form with Dini continuous coefficients 具有Dini连续系数的非发散形式二阶椭圆算子的格林函数估计
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp925
Zhen-Qing Chen, Jie-Ming Wang
{"title":"Green function estimates for second order elliptic operators in non-divergence form with Dini continuous coefficients","authors":"Zhen-Qing Chen, Jie-Ming Wang","doi":"10.1214/23-ejp925","DOIUrl":"https://doi.org/10.1214/23-ejp925","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47076794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Sticky Feller diffusions 粘滞费勒扩散
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp909
Goran Peskir, G. David Roodman
{"title":"Sticky Feller diffusions","authors":"Goran Peskir, G. David Roodman","doi":"10.1214/23-ejp909","DOIUrl":"https://doi.org/10.1214/23-ejp909","url":null,"abstract":"dXt = (bXt+c)I(Xt >0) dt+ √ 2aXt dBt I(Xt =0) dt = 1 μ d` 0 t (X) where b ∈ IR and 0 < c < a are given and fixed, B is a standard Brownian motion, and `(X) is a diffusion local time process of X at 0 , and (ii) the transition density function of X can be expressed in the closed form by means of a convolution integral involving a new special function and a modified Bessel function of the second kind. The new special function embodies the stickiness of X entirely and reduces to the Mittag-Leffler function when b = 0 . We determine a (sticky) boundary condition at zero that characterises the transition density function of X as a unique solution to the Kolmogorov forward/backward equation of X . Letting μ ↓ 0 (absorption) and μ ↑ ∞ (instantaneous reflection) the closed-form expression for the transition density function of X reduces to the ones found by Feller [6] and Molchanov [14] respectively. The results derived for sticky Feller diffusions translate over to yield closed-form expressions for the transition density functions of (a) sticky Cox-Ingersoll-Ross processes and (b) sticky reflecting Vasicek processes that can be used to model slowly reflecting interest rates.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48461047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Fractional Edgeworth expansions for one-dimensional heavy-tailed random variables and applications 一维重尾随机变量的分数阶Edgeworth展开及其应用
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp996
L. Chiarini, M. Jara, W. Ruszel
{"title":"Fractional Edgeworth expansions for one-dimensional heavy-tailed random variables and applications","authors":"L. Chiarini, M. Jara, W. Ruszel","doi":"10.1214/23-ejp996","DOIUrl":"https://doi.org/10.1214/23-ejp996","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44108622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Quantitative Tracy–Widom laws for the largest eigenvalue of generalized Wigner matrices 广义Wigner矩阵最大特征值的定量traci - wisdom律
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1028
Kevin Schnelli, Yuanyuan Xu
{"title":"Quantitative Tracy–Widom laws for the largest eigenvalue of generalized Wigner matrices","authors":"Kevin Schnelli, Yuanyuan Xu","doi":"10.1214/23-ejp1028","DOIUrl":"https://doi.org/10.1214/23-ejp1028","url":null,"abstract":"We show that the fluctuations of the largest eigenvalue of any generalized Wigner matrix H converge to the Tracy–Widom laws at a rate nearly O(N−1∕3), as the matrix dimension N tends to infinity. We allow the variances of the entries of H to have distinct values but of comparable sizes such that ∑iE|hij|2=1. Our result improves the previous rate O(N−2∕9) by Bourgade [8] and the proof relies on the first long-time Green function comparison theorem near the edges without the second moment matching restriction.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135213125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Exceptional points of discrete-time random walks in planar domains 平面域上离散时间随机行走的异常点
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp988
Yoshihiro Abe, Marek Biskup, Sangchul Lee
{"title":"Exceptional points of discrete-time random walks in planar domains","authors":"Yoshihiro Abe, Marek Biskup, Sangchul Lee","doi":"10.1214/23-ejp988","DOIUrl":"https://doi.org/10.1214/23-ejp988","url":null,"abstract":"Given a sequence of lattice approximations DN⊂Z2 of a bounded continuum domain D⊂R2 with the vertices outside DN fused together into one boundary vertex ϱ, we consider discrete-time simple random walks on DN∪{ϱ} run for a time proportional to the expected cover time and describe the scaling limit of the exceptional level sets of the thick, thin, light and avoided points. We show that these are distributed, up a spatially-dependent log-normal factor, as the zero-average Liouville Quantum Gravity measures in D. The limit law of the local time configuration at, and nearby, the exceptional points is determined as well. The results extend earlier work by the first two authors who analyzed the continuous-time problem in the parametrization by the local time at ϱ. A novel uniqueness result concerning divisible random measures and, in particular, Gaussian Multiplicative Chaos, is derived as part of the proofs.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135448135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A criterion and a Cramér–Wold device for quasi-infinite divisibility for discrete multivariate probability laws 离散多元概率律拟无限可除性的判据和cram<s:1> - wold装置
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1032
Ivan Alexeev, Alexey Khartov
{"title":"A criterion and a Cramér–Wold device for quasi-infinite divisibility for discrete multivariate probability laws","authors":"Ivan Alexeev, Alexey Khartov","doi":"10.1214/23-ejp1032","DOIUrl":"https://doi.org/10.1214/23-ejp1032","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135213386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Cutoff for the averaging process on the hypercube and complete bipartite graphs 超立方图和完全二部图上的平均过程的截断
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp993
P. Caputo, Matteo Quattropani, F. Sau
{"title":"Cutoff for the averaging process on the hypercube and complete bipartite graphs","authors":"P. Caputo, Matteo Quattropani, F. Sau","doi":"10.1214/23-ejp993","DOIUrl":"https://doi.org/10.1214/23-ejp993","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43043296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Stochastic sewing in Banach spaces 巴拿赫空间中的随机缝纫
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp918
Khoa Le
{"title":"Stochastic sewing in Banach spaces","authors":"Khoa Le","doi":"10.1214/23-ejp918","DOIUrl":"https://doi.org/10.1214/23-ejp918","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41605983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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