Stochastic Processes and their Applications最新文献_第4页

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

A definition of self-adjoint operators derived from the Schrödinger operator with the white noise potential on the plane 自伴随算子的定义，由平面上具有白噪声势的Schrödinger算子推导而来

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2025-03-27 DOI: 10.1016/j.spa.2025.104642

Naomasa Ueki

{"title":"A definition of self-adjoint operators derived from the Schrödinger operator with the white noise potential on the plane","authors":"Naomasa Ueki","doi":"10.1016/j.spa.2025.104642","DOIUrl":"10.1016/j.spa.2025.104642","url":null,"abstract":"<div><div>For the white noise <span><math><mi>ξ</mi></math></span> on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, an operator corresponding to a limit of <span><math><mrow><mo>−</mo><mi>Δ</mi><mo>+</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>ɛ</mi></mrow></msub><mo>+</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>ɛ</mi></mrow></msub></mrow></math></span> as <span><math><mrow><mi>ɛ</mi><mo>→</mo><mn>0</mn></mrow></math></span> is realized as a self-adjoint operator, where, for each <span><math><mrow><mi>ɛ</mi><mo>></mo><mn>0</mn></mrow></math></span>, <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>ɛ</mi></mrow></msub></math></span> is a constant, <span><math><msub><mrow><mi>ξ</mi></mrow><mrow><mi>ɛ</mi></mrow></msub></math></span> is a smooth approximation of <span><math><mi>ξ</mi></math></span> defined by <span><math><mrow><mo>exp</mo><mrow><mo>(</mo><msup><mrow><mi>ɛ</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>Δ</mi><mo>)</mo></mrow><mi>ξ</mi></mrow></math></span>, and <span><math><mi>Δ</mi></math></span> is the Laplacian. This result is a variant of results obtained by Allez and Chouk, Mouzard, and Ugurcan. The proof in this paper is based on the heat semigroup approach of the paracontrolled calculus, referring the proof by Mouzard. For the obtained operator, the spectral set is shown to be <span><math><mi>R</mi></math></span>.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"186 ","pages":"Article 104642"},"PeriodicalIF":1.1,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734910","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 deviations for empirical measures of self-interacting Markov chains 自相互作用马尔可夫链经验测度的大偏差

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2025-03-27 DOI: 10.1016/j.spa.2025.104640

Amarjit Budhiraja , Adam Waterbury , Pavlos Zoubouloglou

引用次数: 0

Limit theorems for high-dimensional Betti numbers in the multiparameter random simplicial complexes 多参数随机简单复合体中高维Betti数的极限定理

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2025-03-25 DOI: 10.1016/j.spa.2025.104641

Takashi Owada , Gennady Samorodnitsky

引用次数: 0

Multiple and weak Markov properties in Hilbert spaces with applications to fractional stochastic evolution equations 希尔伯特空间中的多重和弱马尔可夫性质及其在分数阶随机演化方程中的应用

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2025-03-25 DOI: 10.1016/j.spa.2025.104639

Kristin Kirchner , Joshua Willems

引用次数: 0

Harmonizable Multifractional Stable Field: Sharp results on sample path behavior 可调和多分数稳定场：关于样本路径行为的尖锐结果

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2025-03-24 DOI: 10.1016/j.spa.2025.104638

Antoine Ayache, Christophe Louckx

{"title":"Harmonizable Multifractional Stable Field: Sharp results on sample path behavior","authors":"Antoine Ayache, Christophe Louckx","doi":"10.1016/j.spa.2025.104638","DOIUrl":"10.1016/j.spa.2025.104638","url":null,"abstract":"<div><div>For about three decades now, there is an increasing interest in study of multifractional processes/fields. The paradigmatic example of them is Multifractional Brownian Field (MBF) over <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>, which is a Gaussian generalization with varying Hurst parameter (the Hurst function) of the well-known Fractional Brownian Motion (FBM). Harmonizable Multifractional Stable Field (HMSF) is a very natural (and maybe the most natural) extension of MBF to the framework of heavy-tailed Symmetric <span><math><mi>α</mi></math></span>-Stable (S<span><math><mi>α</mi></math></span>S) distributions. Many methods related with Gaussian fields fail to work in such a non-Gaussian framework, this is what makes study of HMSF to be difficult. In our article we construct wavelet type random series representations for the S<span><math><mi>α</mi></math></span>S stochastic field generating HMSF and for related fields. Then, under weakened versions of the usual Hölder condition on the Hurst function, we obtain sharp results on sample path behavior of HMSF: optimal global and pointwise moduli of continuity, quasi-optimal pointwise modulus of continuity on a universal event of probability 1 not depending on the location, and an estimate of the behavior at infinity which is optimal when the Hurst function has a limit at infinity to which it converges at a logarithmic rate.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"186 ","pages":"Article 104638"},"PeriodicalIF":1.1,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734909","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 lower bound for pc in range-R bond percolation in four, five and six dimensions 四维、五维和六维r键渗流中pc的下界

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2025-03-20 DOI: 10.1016/j.spa.2025.104637

Jieliang Hong

引用次数: 0