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Stochastic Processes and their Applications最新文献

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Nonparametric estimation of the transition density function for diffusion processes 扩散过程过渡密度函数的非参数估计
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-26 DOI: 10.1016/j.spa.2025.104667
Fabienne Comte , Nicolas Marie
{"title":"Nonparametric estimation of the transition density function for diffusion processes","authors":"Fabienne Comte ,&nbsp;Nicolas Marie","doi":"10.1016/j.spa.2025.104667","DOIUrl":"10.1016/j.spa.2025.104667","url":null,"abstract":"<div><div>We assume that we observe <span><math><mrow><mi>N</mi><mo>∈</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span> independent copies of a diffusion process on a time-interval <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>2</mn><mi>T</mi><mo>]</mo></mrow></math></span>. For a given time <span><math><mrow><mi>t</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow></mrow></math></span>, we estimate the transition density <span><math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>t</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mo>.</mo><mo>)</mo></mrow></mrow></math></span>, namely the conditional density of <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>t</mi><mo>+</mo><mi>s</mi></mrow></msub></math></span> given <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mi>x</mi></mrow></math></span>, under conditions on the diffusion coefficients ensuring that this quantity exists. We use a least squares projection method on a product of finite dimensional spaces, prove risk bounds for the estimator and propose an anisotropic model selection method, relying on several reference norms. A simulation study illustrates the theoretical part for Ornstein–Uhlenbeck or square-root (Cox-Ingersoll-Ross) processes.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"188 ","pages":"Article 104667"},"PeriodicalIF":1.1,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143882892","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: 0
A functional central limit theorem for weighted occupancy processes of the Karlin model Karlin模型加权占用过程的一个泛函中心极限定理
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-25 DOI: 10.1016/j.spa.2025.104665
Jaime Garza, Yizao Wang
{"title":"A functional central limit theorem for weighted occupancy processes of the Karlin model","authors":"Jaime Garza,&nbsp;Yizao Wang","doi":"10.1016/j.spa.2025.104665","DOIUrl":"10.1016/j.spa.2025.104665","url":null,"abstract":"<div><div>A functional central limit theorem is established for weighted occupancy processes of the Karlin model. The weighted occupancy processes take the form of, with <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>j</mi></mrow></msub></math></span> denoting the number of urns with <span><math><mi>j</mi></math></span>-balls after the first <span><math><mi>n</mi></math></span> samplings, <span><math><mrow><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><msub><mrow><mi>a</mi></mrow><mrow><mi>j</mi></mrow></msub><msub><mrow><mi>D</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>j</mi></mrow></msub></mrow></math></span> for a prescribed sequence of real numbers <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>j</mi><mo>∈</mo><mi>N</mi></mrow></msub></math></span>. The main applications are limit theorems for random permutations induced by Chinese restaurant processes with <span><math><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>θ</mi><mo>)</mo></mrow></math></span>-seating with <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mo>,</mo><mi>θ</mi><mo>&gt;</mo><mo>−</mo><mi>α</mi></mrow></math></span>. An example is briefly mentioned here, and full details are provided in an accompanying paper.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"188 ","pages":"Article 104665"},"PeriodicalIF":1.1,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143882890","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: 0
A propagation of chaos result for weakly interacting nonlinear Snell envelopes 弱相互作用非线性Snell包络的混沌传播结果
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-25 DOI: 10.1016/j.spa.2025.104669
Boualem Djehiche , Roxana Dumitrescu , Jia Zeng
{"title":"A propagation of chaos result for weakly interacting nonlinear Snell envelopes","authors":"Boualem Djehiche ,&nbsp;Roxana Dumitrescu ,&nbsp;Jia Zeng","doi":"10.1016/j.spa.2025.104669","DOIUrl":"10.1016/j.spa.2025.104669","url":null,"abstract":"<div><div>In this article, we establish a propagation of chaos result for weakly interacting nonlinear Snell envelopes which converge to a class of mean-field reflected backward stochastic differential equations (BSDEs) with jumps and right-continuous and left-limited obstacle, where the mean-field interaction in terms of the distribution of the <span><math><mi>Y</mi></math></span>-component of the solution enters both the driver and the lower obstacle. Under mild Lipschitz and integrability conditions on the coefficients, we prove existence and uniqueness of the solution to both the mean-field reflected BSDEs with jumps and the corresponding system of weakly interacting particles by using a new approach relying on the characterization of the solution of a mean-field reflected BSDE in terms of a nonlinear optimal stopping problem of mean-field type. We then provide a propagation of chaos result for the whole solution <span><math><mrow><mo>(</mo><mi>Y</mi><mo>,</mo><mi>Z</mi><mo>,</mo><mi>U</mi><mo>,</mo><mi>K</mi><mo>)</mo></mrow></math></span>, which requires new technical results due to the dependence of the obstacle on the solution and the presence of jumps. In particular, we obtain a new law of large number type result for right-continuous and left-limited processes.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"188 ","pages":"Article 104669"},"PeriodicalIF":1.1,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143882891","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: 0
Local asymptotic properties for the growth rate of a jump-type CIR process 跳变型CIR过程增长率的局部渐近性质
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-20 DOI: 10.1016/j.spa.2025.104664
Mohamed Ben Alaya , Ahmed Kebaier , Gyula Pap , Ngoc Khue Tran
{"title":"Local asymptotic properties for the growth rate of a jump-type CIR process","authors":"Mohamed Ben Alaya ,&nbsp;Ahmed Kebaier ,&nbsp;Gyula Pap ,&nbsp;Ngoc Khue Tran","doi":"10.1016/j.spa.2025.104664","DOIUrl":"10.1016/j.spa.2025.104664","url":null,"abstract":"<div><div>In this paper, we consider a one-dimensional jump-type Cox–Ingersoll–Ross process driven by a Brownian motion and a subordinator, whose growth rate is an unknown parameter. Considering the process observed continuously or discretely at high frequency, we derive the local asymptotic properties for the growth rate in both ergodic and non-ergodic cases. Local asymptotic normality (LAN) is proved in the subcritical case, local asymptotic quadraticity (LAQ) is derived in the critical case, and local asymptotic mixed normality (LAMN) is shown in the supercritical case. To obtain these results, techniques of Malliavin calculus and a subtle analysis on the jump structure of the subordinator involving the amplitude of jumps and number of jumps are essentially used.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"187 ","pages":"Article 104664"},"PeriodicalIF":1.1,"publicationDate":"2025-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143867753","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: 0
Speed of convergence and moderate deviations of FPP on random geometric graphs 随机几何图上FPP的收敛速度和适度偏差
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-19 DOI: 10.1016/j.spa.2025.104652
Lucas R. de Lima , Daniel Valesin
{"title":"Speed of convergence and moderate deviations of FPP on random geometric graphs","authors":"Lucas R. de Lima ,&nbsp;Daniel Valesin","doi":"10.1016/j.spa.2025.104652","DOIUrl":"10.1016/j.spa.2025.104652","url":null,"abstract":"<div><div>This study delves into first-passage percolation on random geometric graphs in the supercritical regime, where the graphs exhibit a unique infinite connected component. We investigate properties such as geodesic paths, moderate deviations, and fluctuations, aiming to establish a quantitative shape theorem. Furthermore, we examine fluctuations in geodesic paths and characterize the properties of spanning trees and their semi-infinite paths.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"187 ","pages":"Article 104652"},"PeriodicalIF":1.1,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143867754","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: 0
Lp-solutions of multi-dimensional BSDEs with mean reflection 具有平均反射的多维BSDEs的lp解
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-18 DOI: 10.1016/j.spa.2025.104663
Yue Niu , Baoyou Qu , Falei Wang
{"title":"Lp-solutions of multi-dimensional BSDEs with mean reflection","authors":"Yue Niu ,&nbsp;Baoyou Qu ,&nbsp;Falei Wang","doi":"10.1016/j.spa.2025.104663","DOIUrl":"10.1016/j.spa.2025.104663","url":null,"abstract":"<div><div>The present paper focuses on the investigation of multi-dimensional mean reflected backward stochastic differential equations (BSDEs) in a possibly non-convex reflection domain, whose generator also depends on the marginal probability distributions of the solution <span><math><mrow><mo>(</mo><mi>Y</mi><mo>,</mo><mi>Z</mi><mo>)</mo></mrow></math></span>. Our main idea is to decompose the mean reflected BSDE into a BSDE and a deterministic Skorokhod problem. Then, utilizing <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-estimates for BSDEs and Skorokhod problems, we explore the solvability of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-solutions (<span><math><mrow><mi>p</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>) through fixed-point argument and an approximation approach under both inward normal and oblique reflection scenarios.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"187 ","pages":"Article 104663"},"PeriodicalIF":1.1,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143851716","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: 0
Large deviation estimates for nonlinear filtering with discontinuity and small noise 不连续小噪声非线性滤波的大偏差估计
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-17 DOI: 10.1016/j.spa.2025.104662
Hongjiang Qian , Yanzhao Cao , George Yin
{"title":"Large deviation estimates for nonlinear filtering with discontinuity and small noise","authors":"Hongjiang Qian ,&nbsp;Yanzhao Cao ,&nbsp;George Yin","doi":"10.1016/j.spa.2025.104662","DOIUrl":"10.1016/j.spa.2025.104662","url":null,"abstract":"<div><div>This paper develops large deviation estimates for nonlinear filtering with discontinuity in the drift of the signal and small noise intensities in both the signal and the observations. A variational approach related to Mortensen’s optimization problem is utilized in our analysis. The discontinuity of the drift in the signal naturally arises in many applications, including modeling communication channels with a “hard limiter”. Our results extend the work of Reddy et al. (2022), in which smooth functions were used. To address the discontinuous in the drift of the signal, relaxed controls are used to study the asymptotic fraction of time the controlled signals spend in each half-space divided by the discontinuity hyperplane. Large deviation estimates are established by the weak convergence method using the stochastic control representation for positive functionals of Brownian motions and Laplace asymptotics of the Kallianpur–Striebel formula.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"187 ","pages":"Article 104662"},"PeriodicalIF":1.1,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143843568","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: 0
On the signature of an image 在图像的签名上
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-17 DOI: 10.1016/j.spa.2025.104661
Joscha Diehl , Kurusch Ebrahimi-Fard , Fabian N. Harang , Samy Tindel
{"title":"On the signature of an image","authors":"Joscha Diehl ,&nbsp;Kurusch Ebrahimi-Fard ,&nbsp;Fabian N. Harang ,&nbsp;Samy Tindel","doi":"10.1016/j.spa.2025.104661","DOIUrl":"10.1016/j.spa.2025.104661","url":null,"abstract":"<div><div>Over the past decade, the importance of the 1D signature which can be seen as a functional defined over a path, has been pivotal in both path-wise stochastic calculus and the analysis of time series data. By considering an image as a two-parameter function that takes values in a <span><math><mi>d</mi></math></span>-dimensional space, we introduce an extension of the path signature to images. We address numerous challenges associated with this extension and demonstrate that the 2D signature satisfies a version of Chen’s relation in addition to a shuffle-type product. Furthermore, we show that specific variations of the 2D signature can be recursively defined, thereby satisfying an integral-type equation. We analyze the properties of the proposed signature, such as continuity, invariance to stretching, translation and rotation of the underlying image. Additionally, we establish that the proposed 2D signature over an image satisfies a universal approximation property.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"187 ","pages":"Article 104661"},"PeriodicalIF":1.1,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868643","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: 0
Stable processes with reflections 带反射的稳定过程
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-15 DOI: 10.1016/j.spa.2025.104654
Krzysztof Bogdan , Markus Kunze
{"title":"Stable processes with reflections","authors":"Krzysztof Bogdan ,&nbsp;Markus Kunze","doi":"10.1016/j.spa.2025.104654","DOIUrl":"10.1016/j.spa.2025.104654","url":null,"abstract":"<div><div>We construct a Hunt process that can be described as an isotropic <span><math><mi>α</mi></math></span>-stable Lévy process reflected from the complement of a bounded open Lipschitz set. In fact, we introduce a new analytic method for concatenating Markov processes. It is based on nonlocal Schrödinger perturbations of sub-Markovian transition kernels and the construction of two supermedian functions with different growth rates at infinity. We apply this framework to describe the return distribution and the stationary distribution of the process. To handle the strong Markov property at the reflection time, we introduce a novel ladder process, whose transition semigroup encodes not only the position of the process, but also the number of reflections.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"187 ","pages":"Article 104654"},"PeriodicalIF":1.1,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143843544","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: 0
Explicit multiscale numerical method for super-linear slow-fast stochastic differential equations 超线性慢速随机微分方程的显式多尺度数值方法
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-13 DOI: 10.1016/j.spa.2025.104653
Yuanping Cui , Xiaoyue Li , Xuerong Mao
{"title":"Explicit multiscale numerical method for super-linear slow-fast stochastic differential equations","authors":"Yuanping Cui ,&nbsp;Xiaoyue Li ,&nbsp;Xuerong Mao","doi":"10.1016/j.spa.2025.104653","DOIUrl":"10.1016/j.spa.2025.104653","url":null,"abstract":"<div><div>This manuscript is dedicated to the numerical approximation of super-linear slow-fast stochastic differential equations (SFSDEs). Borrowing the heterogeneous multiscale idea, we propose an explicit multiscale Euler–Maruyama scheme suitable for SFSDEs with locally Lipschitz coefficients using an appropriate truncation technique. By the averaging principle, we establish the strong convergence of the numerical solutions to the exact solutions in the <span><math><mi>p</mi></math></span>th moment. Additionally, under lenient conditions on the coefficients, we also furnish a strong error estimate. In conclusion, we give two illustrative examples and accompanying numerical simulations to affirm the theoretical outcomes.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"187 ","pages":"Article 104653"},"PeriodicalIF":1.1,"publicationDate":"2025-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143843656","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: 0
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