Annals of Applied Probability最新文献_第8页

Convergence to the thermodynamic limit for random-field random surfaces 随机场随机表面热力学极限的收敛性

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2021-05-09 DOI: 10.1214/22-aap1844

P. Dario

引用次数: 3

Optimal stopping with signatures 具有签名的最佳停止

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2021-05-03 DOI: 10.1214/22-aap1814

Christian Bayer, Paul Hager, Sebastian Riedel, J. Schoenmakers

{"title":"Optimal stopping with signatures","authors":"Christian Bayer, Paul Hager, Sebastian Riedel, J. Schoenmakers","doi":"10.1214/22-aap1814","DOIUrl":"https://doi.org/10.1214/22-aap1814","url":null,"abstract":"We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process $X$. We consider classic and randomized stopping times represented by linear and non-linear functionals of the rough path signature $mathbb{X}^{<infty}$ associated to $X$, and prove that maximizing over these classes of signature stopping times, in fact, solves the original optimal stopping problem. Using the algebraic properties of the signature, we can then recast the problem as a (deterministic) optimization problem depending only on the (truncated) expected signature $mathbb{E}left[ mathbb{X}^{le N}_{0,T} right]$. By applying a deep neural network approach to approximate the non-linear signature functionals, we can efficiently solve the optimal stopping problem numerically. The only assumption on the process $X$ is that it is a continuous (geometric) random rough path. Hence, the theory encompasses processes such as fractional Brownian motion, which fail to be either semi-martingales or Markov processes, and can be used, in particular, for American-type option pricing in fractional models, e.g. on financial or electricity markets.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43101412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 16

Dense multigraphon-valued stochastic processes and edge-changing dynamics in the configuration model 配置模型中的稠密多图值随机过程和边变化动力学

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2021-04-27 DOI: 10.1214/22-aap1889

A. Rollin, Zhuohui Zhang

引用次数: 1

The mean-field zero-range process with unbounded monotone rates: Mixing time, cutoff, and Poincaré constant 具有无界单调率的平均场零范围过程:混合时间、截止时间和庞卡罗常数

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2021-04-21 DOI: 10.1214/22-aap1851

Hong-Quan Tran

引用次数: 0

A characterization of martingale-equivalent mixed compound Poisson processes 鞅-等效混合复合泊松过程的表征

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2021-04-01 DOI: 10.1214/20-AAP1604

D. P. Lyberopoulos, N. D. Macheras

引用次数: 1

Large deviations of Kac’s conservative particle system and energy nonconserving solutions to the Boltzmann equation: A counterexample to the predicted rate function Kac守恒粒子系统的大偏差和Boltzmann方程的能量非守恒解：预测速率函数的反例

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2021-03-26 DOI: 10.1214/22-aap1852

Daniel Heydecker

引用次数: 10

Convergence of persistence diagram in the sparse regime 稀疏状态下持久图的收敛性

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2021-03-24 DOI: 10.1214/22-aap1800

Takashi Owada

引用次数: 7

Hellinger and total variation distance in approximating Lévy driven SDEs Hellinger和近似Lévy驱动SDE的总变差距离

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2021-03-17 DOI: 10.1214/22-aap1863

E. Cl'ement

引用次数: 2

Quenched law of large numbers and quenched central limit theorem for multiplayer leagues with ergodic strengths 具有遍历强度的多人联盟的淬灭大数定律和淬灭中心极限定理

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2021-03-01 DOI: 10.1214/22-aap1790

J. Borga, Benedetta Cavalli

{"title":"Quenched law of large numbers and quenched central limit theorem for multiplayer leagues with ergodic strengths","authors":"J. Borga, Benedetta Cavalli","doi":"10.1214/22-aap1790","DOIUrl":"https://doi.org/10.1214/22-aap1790","url":null,"abstract":"We propose and study a new model for competitions, specifically sports multi-player leagues where the initial strengths of the teams are independent i.i.d. random variables that evolve during different days of the league according to independent ergodic processes. The result of each match is random: the probability that a team wins against another team is determined by a function of the strengths of the two teams in the day the match is played. Our model generalizes some previous models studied in the physical and mathematical literature and is defined in terms of different parameters that can be statistically calibrated. We prove a quenched -- conditioning on the initial strengths of the teams -- law of large numbers and a quenched central limit theorem for the number of victories of a team according to its initial strength. To obtain our results, we prove a theorem of independent interest. For a stationary process $xi=(xi_i)_{iin mathbb{N}}$ satisfying a mixing condition and an independent sequence of i.i.d. random variables $(s_i)_{iin mathbb{N}}$, we prove a quenched -- conditioning on $(s_i)_{iinmathbb{N}}$ -- central limit theorem for sums of the form $sum_{i=1}^{n}gleft(xi_i,s_iright)$, where $g$ is a bounded measurable function. We highlight that the random variables $gleft(xi_i,s_iright)$ are not stationary conditioning on $(s_i)_{iinmathbb{N}}$.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46506912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Rates of multivariate normal approximation for statistics in geometric probability 几何概率统计的多元正态逼近率

IF 1.8 2区数学

Annals of Applied Probability Pub Date : 2021-02-28 DOI: 10.1214/22-aap1822

Matthias Schulte, J. Yukich

{"title":"Rates of multivariate normal approximation for statistics in geometric probability","authors":"Matthias Schulte, J. Yukich","doi":"10.1214/22-aap1822","DOIUrl":"https://doi.org/10.1214/22-aap1822","url":null,"abstract":"We employ stabilization methods and second order Poincar'e inequalities to establish rates of multivariate normal convergence for a large class of vectors $(H_s^{(1)},...,H_s^{(m)})$, $s geq 1$, of statistics of marked Poisson processes on $mathbb{R}^d$, $d geq 2$, as the intensity parameter $s$ tends to infinity. Our results are applicable whenever the constituent functionals $H_s^{(i)}$, $iin{1,...,m}$, are expressible as sums of exponentially stabilizing score functions satisfying a moment condition. The rates are for the $d_2$-, $d_3$-, and $d_{convex}$-distances. When we compare with a centered Gaussian random vector, whose covariance matrix is given by the asymptotic covariances, the rates are in general unimprovable and are governed by the rate of convergence of $s^{-1} {rm Cov}( H_s^{(i)}, H_s^{(j)})$, $i,jin{1,...,m}$, to the limiting covariance, shown to be of order $s^{-1/d}$. We use the general results to deduce rates of multivariate normal convergence for statistics arising in random graphs and topological data analysis as well as for multivariate statistics used to test equality of distributions. Some of our results hold for stabilizing functionals of Poisson input on suitable metric spaces.","PeriodicalId":50979,"journal":{"name":"Annals of Applied Probability","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45102554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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