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Stochastic Processes and their Applications最新文献

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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
On Riemann–Liouville type operators, bounded mean oscillation, gradient estimates and approximation on the Wiener space 关于Riemann-Liouville型算子，Wiener空间上的有界平均振荡，梯度估计和逼近
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-12 DOI: 10.1016/j.spa.2025.104651
Stefan Geiss , Nguyen Tran Thuan
{"title":"On Riemann–Liouville type operators, bounded mean oscillation, gradient estimates and approximation on the Wiener space","authors":"Stefan Geiss ,&nbsp;Nguyen Tran Thuan","doi":"10.1016/j.spa.2025.104651","DOIUrl":"10.1016/j.spa.2025.104651","url":null,"abstract":"<div><div>We discuss in a stochastic framework the interplay between Riemann–Liouville type operators applied to stochastic processes, bounded mean oscillation, real interpolation, and approximation. In particular, we investigate the singularity of gradient processes on the Wiener space arising from parabolic PDEs via the Feynman–Kac theory. The singularity is measured in terms of bmo-conditions on the fractional integrated gradient. As an application we treat an approximation problem for stochastic integrals on the Wiener space. In particular, we provide a discrete time hedging strategy for the binary option with a uniform local control of the hedging error under a shortfall constraint.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"187 ","pages":"Article 104651"},"PeriodicalIF":1.1,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143843569","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
Strang splitting for parametric inference in second-order stochastic differential equations 二阶随机微分方程参数推理的奇异分裂
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-09 DOI: 10.1016/j.spa.2025.104650
Predrag Pilipovic , Adeline Samson , Susanne Ditlevsen
{"title":"Strang splitting for parametric inference in second-order stochastic differential equations","authors":"Predrag Pilipovic ,&nbsp;Adeline Samson ,&nbsp;Susanne Ditlevsen","doi":"10.1016/j.spa.2025.104650","DOIUrl":"10.1016/j.spa.2025.104650","url":null,"abstract":"<div><div>We address parameter estimation in second-order stochastic differential equations (SDEs), which are prevalent in physics, biology, and ecology. The second-order SDE is converted to a first-order system by introducing an auxiliary velocity variable, which raises two main challenges. First, the system is hypoelliptic since the noise affects only the velocity, making the Euler–Maruyama estimator ill-conditioned. We propose an estimator based on the Strang splitting scheme to overcome this. Second, since the velocity is rarely observed, we adapt the estimator to partial observations. We present four estimators for complete and partial observations, using the full pseudo-likelihood or only the velocity-based partial pseudo-likelihood. These estimators are intuitive, easy to implement, and computationally fast, and we prove their consistency and asymptotic normality. Our analysis demonstrates that using the full pseudo-likelihood with complete observations reduces the asymptotic variance of the diffusion estimator. With partial observations, the asymptotic variance increases as a result of information loss but remains unaffected by the likelihood choice. However, a numerical study on the Kramers oscillator reveals that using the partial pseudo-likelihood for partial observations yields less biased estimators. We apply our approach to paleoclimate data from the Greenland ice core by fitting the Kramers oscillator model, capturing transitions between metastable states reflecting observed climatic conditions during glacial eras.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"187 ","pages":"Article 104650"},"PeriodicalIF":1.1,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143829599","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
Ancestral lineages for a branching annihilating random walk 分支湮灭随机游走的祖先谱系
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-07 DOI: 10.1016/j.spa.2025.104648
Pascal Oswald
{"title":"Ancestral lineages for a branching annihilating random walk","authors":"Pascal Oswald","doi":"10.1016/j.spa.2025.104648","DOIUrl":"10.1016/j.spa.2025.104648","url":null,"abstract":"<div><div>We study the ancestral lineages of individuals of a stationary discrete-time branching annihilating random walk (BARW) on the <span><math><mi>d</mi></math></span>-dimensional lattice <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. Each individual produces a Poissonian number of offspring with mean <span><math><mi>μ</mi></math></span> which then jump independently to a uniformly chosen site with a fixed distance <span><math><mi>R</mi></math></span> of their parent. Should two or more particles jump to the same site, all particles at that site get annihilated. By interpreting the ancestral lineage of such an individual as a random walk in a dynamical random environment, we obtain a law of large numbers and a functional central limit theorem for the ancestral lineage whenever the model parameters satisfy <span><math><mrow><mi>μ</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>R</mi><mo>=</mo><mi>R</mi><mrow><mo>(</mo><mi>μ</mi><mo>)</mo></mrow></mrow></math></span> is large enough.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"187 ","pages":"Article 104648"},"PeriodicalIF":1.1,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143835136","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
Well-posedness of a reaction–diffusion model with stochastic dynamical boundary conditions 具有随机动力学边界条件的反应扩散模型的适定性
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-07 DOI: 10.1016/j.spa.2025.104646
Mario Maurelli , Daniela Morale , Stefania Ugolini
{"title":"Well-posedness of a reaction–diffusion model with stochastic dynamical boundary conditions","authors":"Mario Maurelli ,&nbsp;Daniela Morale ,&nbsp;Stefania Ugolini","doi":"10.1016/j.spa.2025.104646","DOIUrl":"10.1016/j.spa.2025.104646","url":null,"abstract":"<div><div>We study the well-posedness of a nonlinear reaction diffusion partial differential equation system on the half-line coupled with a stochastic dynamical boundary condition, a random system arising from the description of the chemical reaction of sulphur dioxide with calcium carbonate stones. The boundary condition is given by a Jacobi process, solution to a stochastic differential equation with a mean-reverting drift and a bounded diffusion coefficient. The main result is the global existence and the pathwise uniqueness of mild solutions. The proof relies on a splitting strategy, which allows to deal with the low regularity of the dynamical boundary condition.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"186 ","pages":"Article 104646"},"PeriodicalIF":1.1,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808735","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
Inference in nonlinear random fields and non-asymptotic rates for threshold variance estimators under sparse dependence 非线性随机场的推理和稀疏依赖下阈值方差估计的非渐近率
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-07 DOI: 10.1016/j.spa.2025.104649
Ansgar Steland
{"title":"Inference in nonlinear random fields and non-asymptotic rates for threshold variance estimators under sparse dependence","authors":"Ansgar Steland","doi":"10.1016/j.spa.2025.104649","DOIUrl":"10.1016/j.spa.2025.104649","url":null,"abstract":"<div><div>Inference based on the (functional) central limit theorem for nonlinear random fields is studied and generalized to the nonstationary case. For this purpose, nonparametric estimation of the variance of partial sums is studied in depth including a class of soft-thresholding estimators. Nonasymptotic convergence rates for all estimators are established. It is shown that threshold estimation is superior in terms of the convergence rate under a mild sparseness condition on the spatial covariance structure. The results also cover estimators calculated from residuals. Applications to hypothesis testing to detect effects such as tumors in CT images, regression models with external regressors, and sparse convolutional network layers are discussed.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"186 ","pages":"Article 104649"},"PeriodicalIF":1.1,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143823863","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
Long run convergence of discrete-time interacting particle systems of the McKean–Vlasov type McKean-Vlasov型离散时间相互作用粒子系统的长期收敛
IF 1.1 2区 数学
Stochastic Processes and their Applications Pub Date : 2025-04-06 DOI: 10.1016/j.spa.2025.104647
Pascal Bianchi , Walid Hachem , Victor Priser
{"title":"Long run convergence of discrete-time interacting particle systems of the McKean–Vlasov type","authors":"Pascal Bianchi ,&nbsp;Walid Hachem ,&nbsp;Victor Priser","doi":"10.1016/j.spa.2025.104647","DOIUrl":"10.1016/j.spa.2025.104647","url":null,"abstract":"<div><div>We consider a discrete-time system of <span><math><mi>n</mi></math></span> coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the particles. We study the doubly asymptotic regime where both the number of iterations and the number <span><math><mi>n</mi></math></span> of particles tend to infinity, without any constraint on the relative rates of convergence of these two parameters. We establish that the empirical measure of the interpolated trajectories of the particles converges in probability, in an ergodic sense, to the set of recurrent McKean–Vlasov distributions. We also consider the pointwise convergence of the empirical measures of the particles. We consider the example of the granular media equation, where the particles are shown to converge to a critical point of the Helmholtz energy.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"186 ","pages":"Article 104647"},"PeriodicalIF":1.1,"publicationDate":"2025-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815876","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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