Stochastic Processes and their Applications最新文献_第5页

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

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 , Adeline Samson , 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

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

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

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

引用次数: 0

Lévy models amenable to efficient calculations 适合高效计算的莱维模型

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2025-04-03 DOI: 10.1016/j.spa.2025.104636

Svetlana Boyarchenko , Sergei Levendorskiĭ

{"title":"Lévy models amenable to efficient calculations","authors":"Svetlana Boyarchenko , Sergei Levendorskiĭ","doi":"10.1016/j.spa.2025.104636","DOIUrl":"10.1016/j.spa.2025.104636","url":null,"abstract":"<div><div>In our previous publications (IJTAF 2019, Math. Finance 2020), we introduced a general class of SINH-regular processes and demonstrated that efficient numerical methods for the evaluation of the Wiener–Hopf factors and various probability distributions (prices of options of several types) in Lévy models can be developed using only a few general properties of the characteristic exponent <span><math><mi>ψ</mi></math></span>. Essentially all popular Lévy processes enjoy these properties. In the present paper, we define classes of Stieltjes–Lévy processes (SL-processes) as processes with completely monotone Lévy densities of positive and negative jumps, and signed Stieltjes–Lévy processes (sSL-processes) as processes with densities representable as differences of completely monotone densities. We demonstrate that (1) all crucial properties of <span><math><mi>ψ</mi></math></span> are consequences of a certain representation of the characteristic exponent in terms of a pair of Stieltjes measures or a pair of differences of two Stieltjes measures (SL- and sSL-processes); (2) essentially all popular processes other than Merton’s model and Meixner processes are SL-processes; (3) Meixner processes are sSL-processes; (4) under a natural symmetry condition, essentially all popular classes of Lévy processes are SL- or sSL-subordinated Brownian motion. We use the properties of (s)SL-processes to derive new formulas for the Wiener–Hopf factors <span><math><msubsup><mrow><mi>ϕ</mi></mrow><mrow><mi>q</mi></mrow><mrow><mo>±</mo></mrow></msubsup></math></span> for small <span><math><mi>q</mi></math></span> in terms of the absolute continuous components of SL-measures and their densities, and calculate the leading terms of the survival probability also in terms of the absolute continuous components of SL-measures and their densities. The lower tail probability is calculated for more general classes of SINH-regular processes.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"186 ","pages":"Article 104636"},"PeriodicalIF":1.1,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143830195","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

Stochastic chemical reaction networks with discontinuous limits and AIMD processes 具有不连续极限的随机化学反应网络与AIMD过程

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2025-04-03 DOI: 10.1016/j.spa.2025.104643

Lucie Laurence , Philippe Robert

{"title":"Stochastic chemical reaction networks with discontinuous limits and AIMD processes","authors":"Lucie Laurence , Philippe Robert","doi":"10.1016/j.spa.2025.104643","DOIUrl":"10.1016/j.spa.2025.104643","url":null,"abstract":"<div><div>In this paper we study a class of stochastic chemical reaction networks (CRNs) for which chemical species are created by a sequence of chain reactions. We prove that under some convenient conditions on the initial state, some of these networks exhibit a discrete-induced transitions (DIT) property: isolated, random, events have a direct impact on the macroscopic state of the process. Although this phenomenon has already been noticed in several CRNs, in auto-catalytic networks in the literature of physics in particular, there are up to now few rigorous studies in this domain. A scaling analysis of several cases of such CRNs with several classes of initial states is achieved. The DIT property is investigated for the case of a CRN with four nodes. We show that on the normal timescale and for a subset of (large) initial states and for convenient Skorohod topologies, the scaled process converges in distribution to a Markov process with jumps, an Additive Increase/Multiplicative Decrease (AIMD) process. This asymptotically discontinuous limiting behavior is a consequence of a DIT property due to random, local, blowups of jumps occurring during small time intervals. With an explicit representation of invariant measures of AIMD processes and time-change arguments, we show that, with a speed-up of the timescale, the scaled process is converging in distribution to a continuous deterministic function. The DIT property analyzed in this paper is connected to a simple chain reaction between three chemical species and is therefore likely to be a quite generic phenomenon for a large class of CRNs.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"186 ","pages":"Article 104643"},"PeriodicalIF":1.1,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777273","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

Stationary fluctuations for a multi-species zero range process with long jumps 具有长跳跃的多物种零距离过程的平稳波动

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2025-04-02 DOI: 10.1016/j.spa.2025.104645

Linjie Zhao

引用次数: 0

α-stable Lévy processes entering the half space or a slab α-稳定的lsamy过程进入半空间或平板

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2025-03-28 DOI: 10.1016/j.spa.2025.104644

Andreas E. Kyprianou , Sonny Medina , Juan Carlos Pardo

{"title":"α-stable Lévy processes entering the half space or a slab","authors":"Andreas E. Kyprianou , Sonny Medina , Juan Carlos Pardo","doi":"10.1016/j.spa.2025.104644","DOIUrl":"10.1016/j.spa.2025.104644","url":null,"abstract":"<div><div>Recently a series of publications, including e.g. (Kyprianou, 2016 <span><span>[1]</span></span>; Kyprianou et al., 2018 <span><span>[2]</span></span>; Kyprianou et al., 2019; Kyprianou et al., 2014; Kyprianou and Pardo, 2022), considered a number of new fluctuation identities for <span><math><mi>α</mi></math></span>-stable Lévy processes in one and higher dimensions by appealing to underlying Lamperti-type path decompositions. In the setting of <span><math><mi>d</mi></math></span>-dimensional isotropic processes, (Kyprianou et al., 2019) in particular, developed so called <span><math><mi>n</mi></math></span>-tuple laws for first entrance and exit of balls. Fundamental to these works is the notion that the paths can be decomposed via generalised spherical polar coordinates revealing an underlying Markov Additive Process (MAP) for which a more advanced form of excursion theory (in the sense of Maisonneuve (1975)) can be exploited.</div><div>Inspired by this approach, we give a different decomposition of the <span><math><mi>d</mi></math></span>-dimensional isotropic <span><math><mi>α</mi></math></span>-stable Lévy processes in terms of orthogonal coordinates. Accordingly we are able to develop a number of <span><math><mi>n</mi></math></span>-tuple laws for first entrance into a half-space bounded by an <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span> hyperplane, expanding on existing results of (Byczkowski et al., 2009; Tamura and Tanaka, 2008). This gives us the opportunity to numerically construct the law of first entry of the process into a slab of the form <span><math><mrow><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span> using a ‘walk-on-half-spaces’ Monte Carlo approach in the spirit of the ‘walk-on-spheres’ Monte Carlo method given in Kyprianou et al. (2018).</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"186 ","pages":"Article 104644"},"PeriodicalIF":1.1,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808734","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