Pub Date : 2024-11-26DOI: 10.1016/j.spa.2024.104469
Orphée Collin , Serguei Popov
We prove sharp asymptotic estimates for the rate of escape of the two-dimensional simple random walk conditioned to avoid a fixed finite set. We derive it from asymptotics available for the continuous analogue of this process (Collin and Comets, 2022), with the help of a KMT-type coupling adapted to this setup.
{"title":"Rate of escape of the conditioned two-dimensional simple random walk","authors":"Orphée Collin , Serguei Popov","doi":"10.1016/j.spa.2024.104469","DOIUrl":"10.1016/j.spa.2024.104469","url":null,"abstract":"<div><div>We prove sharp asymptotic estimates for the rate of escape of the two-dimensional simple random walk conditioned to avoid a fixed finite set. We derive it from asymptotics available for the continuous analogue of this process (Collin and Comets, 2022), with the help of a KMT-type coupling adapted to this setup.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"179 ","pages":"Article 104469"},"PeriodicalIF":1.1,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142720072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-23DOI: 10.1016/j.spa.2024.104534
Bingyao Wu , Jie-Xiang Zhu
Fix an irrational number . Let be independent, identically distributed, integer-valued random variables with characteristic function , and let be the partial sums. Consider the random walk on the torus, where denotes the fractional part. We study the long time asymptotic behavior of the empirical measure of this random walk to the uniform distribution under the general -Wasserstein distance. Our results show that the Wasserstein convergence rate depends on the Diophantine properties of and the Hölder continuity of the characteristic function at the origin, and there is an interesting critical phenomenon that will occur. The proof is based on the PDE approach developed by L. Ambrosio, F. Stra and D. Trevisan in Ambrosio et al. (2019) and the continued fraction representation of the irrational number .
{"title":"Wasserstein convergence rates for empirical measures of random subsequence of {nα}","authors":"Bingyao Wu , Jie-Xiang Zhu","doi":"10.1016/j.spa.2024.104534","DOIUrl":"10.1016/j.spa.2024.104534","url":null,"abstract":"<div><div>Fix an irrational number <span><math><mi>α</mi></math></span>. Let <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo></mrow></math></span> be independent, identically distributed, integer-valued random variables with characteristic function <span><math><mi>φ</mi></math></span>, and let <span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></math></span> be the partial sums. Consider the random walk <span><math><msub><mrow><mrow><mo>{</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mi>α</mi><mo>}</mo></mrow></mrow><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></msub></math></span> on the torus, where <span><math><mrow><mo>{</mo><mi>⋅</mi><mo>}</mo></mrow></math></span> denotes the fractional part. We study the long time asymptotic behavior of the empirical measure of this random walk to the uniform distribution under the general <span><math><mi>p</mi></math></span>-Wasserstein distance. Our results show that the Wasserstein convergence rate depends on the Diophantine properties of <span><math><mi>α</mi></math></span> and the Hölder continuity of the characteristic function <span><math><mi>φ</mi></math></span> at the origin, and there is an interesting critical phenomenon that will occur. The proof is based on the PDE approach developed by L. Ambrosio, F. Stra and D. Trevisan in Ambrosio et al. (2019) and the continued fraction representation of the irrational number <span><math><mi>α</mi></math></span>.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"181 ","pages":"Article 104534"},"PeriodicalIF":1.1,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722995","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}
Pub Date : 2024-11-22DOI: 10.1016/j.spa.2024.104535
Aurélien Alfonsi
This work defines and studies one-dimensional convolution kernels that preserve nonnegativity. When the past dynamics of a process is integrated with a convolution kernel like in Stochastic Volterra Equations or in the jump intensity of Hawkes processes, this property allows to get the nonnegativity of the integral. We give characterizations of these kernels and show in particular that completely monotone kernels preserve nonnegativity. We then apply these results to analyze the stochastic invariance of a closed convex set by Stochastic Volterra Equations. We also get a comparison result in dimension one. Last, when the kernel is a positive linear combination of decaying exponential functions, we present a second order approximation scheme for the weak error that stays in the closed convex domain under suitable assumptions. We apply these results to the rough Heston model and give numerical illustrations.
{"title":"Nonnegativity preserving convolution kernels. Application to Stochastic Volterra Equations in closed convex domains and their approximation","authors":"Aurélien Alfonsi","doi":"10.1016/j.spa.2024.104535","DOIUrl":"10.1016/j.spa.2024.104535","url":null,"abstract":"<div><div>This work defines and studies one-dimensional convolution kernels that preserve nonnegativity. When the past dynamics of a process is integrated with a convolution kernel like in Stochastic Volterra Equations or in the jump intensity of Hawkes processes, this property allows to get the nonnegativity of the integral. We give characterizations of these kernels and show in particular that completely monotone kernels preserve nonnegativity. We then apply these results to analyze the stochastic invariance of a closed convex set by Stochastic Volterra Equations. We also get a comparison result in dimension one. Last, when the kernel is a positive linear combination of decaying exponential functions, we present a second order approximation scheme for the weak error that stays in the closed convex domain under suitable assumptions. We apply these results to the rough Heston model and give numerical illustrations.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"181 ","pages":"Article 104535"},"PeriodicalIF":1.1,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The geometry of Arithmetic Random Waves has been extensively investigated in the last fifteen years, starting from the seminal papers (Rudnick and Wigman, 2008; Oravecz et al., 2008). In this paper we study the correlation structure among different functionals such as nodal length, boundary length of excursion sets, and the number of intersection of nodal sets with deterministic curves in different classes; the amount of correlation depends in a subtle fashion from the values of the thresholds considered and the symmetry properties of the deterministic curves. In particular, we prove the existence of resonant pairs of threshold values where the asymptotic correlation is full, that is, at such values one functional can be perfectly predicted from the other in the high energy limit. We focus mainly on the 2-dimensional case but we discuss some specific extensions to dimension 3.
{"title":"Correlation structure and resonant pairs for arithmetic random waves","authors":"Valentina Cammarota , Riccardo W. Maffucci , Domenico Marinucci , Maurizia Rossi","doi":"10.1016/j.spa.2024.104525","DOIUrl":"10.1016/j.spa.2024.104525","url":null,"abstract":"<div><div>The geometry of Arithmetic Random Waves has been extensively investigated in the last fifteen years, starting from the seminal papers (Rudnick and Wigman, 2008; Oravecz et al., 2008). In this paper we study the correlation structure among different functionals such as nodal length, boundary length of excursion sets, and the number of intersection of nodal sets with deterministic curves in different classes; the amount of correlation depends in a subtle fashion from the values of the thresholds considered and the symmetry properties of the deterministic curves. In particular, we prove the existence of <em>resonant pairs</em> of threshold values where the asymptotic correlation is full, that is, at such values one functional can be perfectly predicted from the other in the high energy limit. We focus mainly on the 2-dimensional case but we discuss some specific extensions to dimension 3.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"181 ","pages":"Article 104525"},"PeriodicalIF":1.1,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-14DOI: 10.1016/j.spa.2024.104524
S. Bourguin , K. Spiliopoulos
We study fluctuations of small noise multiscale diffusions around their homogenized deterministic limit. We derive quantitative rates of convergence of the fluctuation processes to their Gaussian limits in the appropriate Wasserstein metric requiring detailed estimates of the first and second order Malliavin derivative of the slow component. We study a fully coupled system and the derivation of the quantitative rates of convergence depends on a very careful decomposition of the first and second Malliavin derivatives of the slow and fast component to terms that have different rates of convergence depending on the strength of the noise and timescale separation parameter.
{"title":"Quantitative fluctuation analysis of multiscale diffusion systems via Malliavin calculus","authors":"S. Bourguin , K. Spiliopoulos","doi":"10.1016/j.spa.2024.104524","DOIUrl":"10.1016/j.spa.2024.104524","url":null,"abstract":"<div><div>We study fluctuations of small noise multiscale diffusions around their homogenized deterministic limit. We derive quantitative rates of convergence of the fluctuation processes to their Gaussian limits in the appropriate Wasserstein metric requiring detailed estimates of the first and second order Malliavin derivative of the slow component. We study a fully coupled system and the derivation of the quantitative rates of convergence depends on a very careful decomposition of the first and second Malliavin derivatives of the slow and fast component to terms that have different rates of convergence depending on the strength of the noise and timescale separation parameter.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"180 ","pages":"Article 104524"},"PeriodicalIF":1.1,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659290","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}
Pub Date : 2024-11-14DOI: 10.1016/j.spa.2024.104523
Florencia Leonardi , Magno T.F. Severino
We propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector. By global criterion, we mean optimizing a function over the set of possible graphs, eliminating the need to estimate individual neighborhoods and subsequently combine them to estimate the graph. We prove the almost sure convergence of the graph estimator. This convergence holds, provided the data is a realization of a multivariate stochastic process that satisfies a polynomial mixing condition. These are the first results to show the consistency of a model selection criterion for Markov random fields on graphs under non-independent data.
{"title":"Model selection for Markov random fields on graphs under a mixing condition","authors":"Florencia Leonardi , Magno T.F. Severino","doi":"10.1016/j.spa.2024.104523","DOIUrl":"10.1016/j.spa.2024.104523","url":null,"abstract":"<div><div>We propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector. By global criterion, we mean optimizing a function over the set of possible graphs, eliminating the need to estimate individual neighborhoods and subsequently combine them to estimate the graph. We prove the almost sure convergence of the graph estimator. This convergence holds, provided the data is a realization of a multivariate stochastic process that satisfies a polynomial mixing condition. These are the first results to show the consistency of a model selection criterion for Markov random fields on graphs under non-independent data.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"180 ","pages":"Article 104523"},"PeriodicalIF":1.1,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698094","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}
Pub Date : 2024-11-13DOI: 10.1016/j.spa.2024.104522
Alessandra Faggionato
We prove a multidimensional ergodic theorem with weighted averages for the action of the group on a probability space. At level weights are of the form , , for real functions decaying suitably fast. We discuss applications to random measures and to quenched stochastic homogenization of random walks on simple point processes with long-range random jump rates, allowing to remove the technical Assumption (A9) from [Faggionato 2023, Theorem 4.4]. This last result concerns also some semigroup and resolvent convergence particularly relevant for the derivation of the quenched hydrodynamic limit of interacting particle systems via homogenization and duality. As a consequence we show that also the quenched hydrodynamic limit of the symmetric simple exclusion process on point processes stated in [Faggionato 2022, Theorem 4.1] remains valid when removing the above mentioned Assumption (A9).
{"title":"An ergodic theorem with weights and applications to random measures, homogenization and hydrodynamics","authors":"Alessandra Faggionato","doi":"10.1016/j.spa.2024.104522","DOIUrl":"10.1016/j.spa.2024.104522","url":null,"abstract":"<div><div>We prove a multidimensional ergodic theorem with weighted averages for the action of the group <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> on a probability space. At level <span><math><mi>n</mi></math></span> weights are of the form <span><math><mrow><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mi>d</mi></mrow></msup><mi>ψ</mi><mrow><mo>(</mo><mi>j</mi><mo>/</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>j</mi><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></math></span>, for real functions <span><math><mi>ψ</mi></math></span> decaying suitably fast. We discuss applications to random measures and to quenched stochastic homogenization of random walks on simple point processes with long-range random jump rates, allowing to remove the technical Assumption (A9) from [Faggionato 2023, Theorem 4.4]. This last result concerns also some semigroup and resolvent convergence particularly relevant for the derivation of the quenched hydrodynamic limit of interacting particle systems via homogenization and duality. As a consequence we show that also the quenched hydrodynamic limit of the symmetric simple exclusion process on point processes stated in [Faggionato 2022, Theorem 4.1] remains valid when removing the above mentioned Assumption (A9).</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"180 ","pages":"Article 104522"},"PeriodicalIF":1.1,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698093","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}
Pub Date : 2024-11-05DOI: 10.1016/j.spa.2024.104519
Vladislav Vysotsky
We study the asymptotic behaviour of the most likely trajectories of a planar random walk that result in large deviations of the area of their convex hull. If the Laplace transform of the increments is finite on , such a scaled limit trajectory solves the inhomogeneous anisotropic isoperimetric problem for the convex hull, where the usual length of is replaced by the large deviations rate functional and is the rate function of the increments. Assuming that the distribution of increments is not supported on a half-plane, we show that the optimal trajectories are convex and satisfy the Euler–Lagrange equation, which we solve explicitly for every . The shape of these trajectories resembles the optimizers in the isoperimetric inequality for the Minkowski plane, found by Busemann (1947).
我们研究了平面随机漫步最可能轨迹的渐近行为，这些轨迹会导致其凸壳面积出现较大偏差。如果增量的拉普拉斯变换在 R2 上是有限的，那么这样的缩放极限轨迹 h 解决了凸壳的非均质各向异性等距问题，其中 h 的通常长度由大偏差率函数 ∫01I(h′(t))dt 代替，I 是增量的率函数。假定增量的分布不在半平面上，我们将证明最优轨迹是凸的，并且满足欧拉-拉格朗日方程，我们对每个 I 都进行了显式求解。
{"title":"The isoperimetric problem for convex hulls and large deviations rate functionals of random walks","authors":"Vladislav Vysotsky","doi":"10.1016/j.spa.2024.104519","DOIUrl":"10.1016/j.spa.2024.104519","url":null,"abstract":"<div><div>We study the asymptotic behaviour of the most likely trajectories of a planar random walk that result in large deviations of the area of their convex hull. If the Laplace transform of the increments is finite on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, such a scaled limit trajectory <span><math><mi>h</mi></math></span> solves the inhomogeneous anisotropic isoperimetric problem for the convex hull, where the usual length of <span><math><mi>h</mi></math></span> is replaced by the large deviations rate functional <span><math><mrow><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><mi>I</mi><mrow><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><mi>d</mi><mi>t</mi></mrow></math></span> and <span><math><mi>I</mi></math></span> is the rate function of the increments. Assuming that the distribution of increments is not supported on a half-plane, we show that the optimal trajectories are convex and satisfy the Euler–Lagrange equation, which we solve explicitly for every <span><math><mi>I</mi></math></span>. The shape of these trajectories resembles the optimizers in the isoperimetric inequality for the Minkowski plane, found by Busemann (1947).</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"180 ","pages":"Article 104519"},"PeriodicalIF":1.1,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-04DOI: 10.1016/j.spa.2024.104521
Yubo Shuai
Motivated by the goal of understanding the genealogy of a sample from an expanding population in the plane, we consider coalescing Brownian motion on the circle. For this model, we establish a weak law of large numbers for the site frequency spectrum. A parallel result holds for a localized version where the genealogy is modeled by coalescing Brownian motion on the line.
{"title":"The site frequency spectrum for coalescing Brownian motion","authors":"Yubo Shuai","doi":"10.1016/j.spa.2024.104521","DOIUrl":"10.1016/j.spa.2024.104521","url":null,"abstract":"<div><div>Motivated by the goal of understanding the genealogy of a sample from an expanding population in the plane, we consider coalescing Brownian motion on the circle. For this model, we establish a weak law of large numbers for the site frequency spectrum. A parallel result holds for a localized version where the genealogy is modeled by coalescing Brownian motion on the line.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"180 ","pages":"Article 104521"},"PeriodicalIF":1.1,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-02DOI: 10.1016/j.spa.2024.104520
Ben Hambly , Julian Meier , Andreas Søjmark
We consider a system of particles undergoing correlated diffusion with elastic boundary conditions on the half-line in the limit as the number of particles goes to infinity. We establish existence and uniqueness for the limiting empirical measure valued process for the surviving particles, which is a weak form for an SPDE with a noisy Robin boundary condition satisfied by the particle density. We show that this density process has good -regularity properties in the interior of the domain but may exhibit singularities on the boundary at a dense set of times. We make connections to the corresponding absorbing and reflecting SPDEs as the elastic parameter varies.
我们考虑了一个粒子系统，该粒子系统在粒子数量达到无穷大的极限时，在半线上进行相关扩散并具有弹性边界条件。我们建立了存活粒子的极限经验度量值过程的存在性和唯一性，该过程是粒子密度满足噪声 Robin 边界条件的 SPDE 的弱形式。我们证明，这一密度过程在域内部具有良好的 L2-正则性，但在密集时间集上可能会在边界上出现奇点。随着弹性参数的变化，我们将其与相应的吸收和反射 SPDE 联系起来。
{"title":"An SPDE with Robin-type boundary for a system of elastically killed diffusions on the positive half-line","authors":"Ben Hambly , Julian Meier , Andreas Søjmark","doi":"10.1016/j.spa.2024.104520","DOIUrl":"10.1016/j.spa.2024.104520","url":null,"abstract":"<div><div>We consider a system of particles undergoing correlated diffusion with elastic boundary conditions on the half-line in the limit as the number of particles goes to infinity. We establish existence and uniqueness for the limiting empirical measure valued process for the surviving particles, which is a weak form for an SPDE with a noisy Robin boundary condition satisfied by the particle density. We show that this density process has good <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-regularity properties in the interior of the domain but may exhibit singularities on the boundary at a dense set of times. We make connections to the corresponding absorbing and reflecting SPDEs as the elastic parameter varies.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"179 ","pages":"Article 104520"},"PeriodicalIF":1.1,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142664023","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}
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