Stochastic partial differential equations : analysis and computations最新文献

Non-Gaussianity of invariant measures to SPDEs in Da Prato-Debussche regime. Da Prato-Debussche区域spde不变测度的非高斯性。

Stochastic partial differential equations : analysis and computations Pub Date : 2026-01-01 Epub Date: 2025-06-19 DOI: 10.1007/s40072-025-00370-3

Ajay Chandra, Ilya Chevyrev

引用次数: 0

An extrapolation result in the variational setting: improved regularity, compactness, and applications to quasilinear systems. 外推结果在变分设置：改进的规则性，紧凑性，并应用于拟线性系统。

Stochastic partial differential equations : analysis and computations Pub Date : 2025-01-01 Epub Date: 2025-07-11 DOI: 10.1007/s40072-025-00378-9

Sebastian Bechtel, Mark Veraar

{"title":"An extrapolation result in the variational setting: improved regularity, compactness, and applications to quasilinear systems.","authors":"Sebastian Bechtel, Mark Veraar","doi":"10.1007/s40072-025-00378-9","DOIUrl":"10.1007/s40072-025-00378-9","url":null,"abstract":"In this paper we consider the variational setting for SPDE on a Gelfand triple <math><mrow><mo>(</mo> <mi>V</mi> <mo>,</mo> <mi>H</mi> <mo>,</mo> <msup><mi>V</mi> <mo>∗</mo></msup> <mo>)</mo></mrow> </math> . Under the standard conditions on a linear coercive pair (A, B), and a symmetry condition on A we manage to extrapolate the classical <math><msup><mtext>L</mtext> <mn>2</mn></msup> </math> -estimates in time to <math><msup><mtext>L</mtext> <mi>p</mi></msup> </math> -estimates for some <math><mrow><mi>p</mi> <mo>></mo> <mn>2</mn></mrow> </math> without any further conditions on (A, B). As a consequence we obtain several other a priori regularity results of the paths of the solution. Under the assumption that V embeds compactly into H, we derive a universal compactness result quantifying over all (A, B). As an application of the compactness result we prove global existence of weak solutions to a system of second order quasi-linear equations.","PeriodicalId":74872,"journal":{"name":"Stochastic partial differential equations : analysis and computations","volume":"13 4","pages":"2000-2038"},"PeriodicalIF":0.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12589295/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145484033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Counterexamples to regularities for the derivative processes associated to stochastic evolution equations. 与随机演化方程相关的导数过程规律的反例。

Stochastic partial differential equations : analysis and computations Pub Date : 2025-01-01 Epub Date: 2025-02-04 DOI: 10.1007/s40072-024-00342-z

Mario Hefter, Arnulf Jentzen, Ryan Kurniawan

{"title":"Counterexamples to regularities for the derivative processes associated to stochastic evolution equations.","authors":"Mario Hefter, Arnulf Jentzen, Ryan Kurniawan","doi":"10.1007/s40072-024-00342-z","DOIUrl":"https://doi.org/10.1007/s40072-024-00342-z","url":null,"abstract":"In the recent years there has been an increased interest in studying regularity properties of the derivatives of semilinear parabolic stochastic evolution equations (SEEs) with respect to their initial values. In particular, in the scientific literature it has been shown for every natural number <math><mrow><mi>n</mi> <mo>∈</mo> <mi>N</mi></mrow> </math> that if the nonlinear drift coefficient and the nonlinear diffusion coefficient of the considered SEE are n-times continuously Fréchet differentiable, then the solution of the considered SEE is also n-times continuously Fréchet differentiable with respect to its initial value and the corresponding derivative processes satisfy a suitable regularity property in the sense that the n-th derivative process can be extended continuously to n-linear operators on negative Sobolev-type spaces with regularity parameters <math> <mrow><msub><mi>δ</mi> <mn>1</mn></msub> <mo>,</mo> <msub><mi>δ</mi> <mn>2</mn></msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub><mi>δ</mi> <mi>n</mi></msub> <mo>∈</mo> <mrow><mo>[</mo> <mn>0</mn> <mo>,</mo> <mi>∞</mi> <mo>)</mo></mrow> </mrow> </math> provided that the condition <math> <mrow><msubsup><mo>∑</mo> <mrow><mi>i</mi> <mo>=</mo> <mn>1</mn></mrow> <mi>n</mi></msubsup> <msub><mi>δ</mi> <mi>i</mi></msub> <mo><</mo> <mfrac><mn>1</mn> <mn>2</mn></mfrac> </mrow> </math> is satisfied. The main contribution of this paper is to reveal that this condition can essentially not be relaxed.","PeriodicalId":74872,"journal":{"name":"Stochastic partial differential equations : analysis and computations","volume":"13 2","pages":"1097-1126"},"PeriodicalIF":0.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12095460/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144144893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An additive-noise approximation to Keller-Segel-Dean-Kawasaki dynamics: local well-posedness of paracontrolled solutions. Keller-Segel-Dean-Kawasaki动力学的加性噪声逼近：副控制解的局部适定性。

Stochastic partial differential equations : analysis and computations Pub Date : 2025-01-01 Epub Date: 2025-01-24 DOI: 10.1007/s40072-024-00343-y

Adrian Martini, Avi Mayorcas

引用次数: 0

Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise. 高斯噪声驱动下随机分数阶演化方程温和解的一些近似结果。

Stochastic partial differential equations : analysis and computations Pub Date : 2023-01-01 Epub Date: 2022-04-26 DOI: 10.1007/s40072-022-00250-0

K Fahim, E Hausenblas, M Kovács

{"title":"Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise.","authors":"K Fahim, E Hausenblas, M Kovács","doi":"10.1007/s40072-022-00250-0","DOIUrl":"10.1007/s40072-022-00250-0","url":null,"abstract":"We investigate the quality of space approximation of a class of stochastic integral equations of convolution type with Gaussian noise. Such equations arise, for example, when considering mild solutions of stochastic fractional order partial differential equations but also when considering mild solutions of classical stochastic partial differential equations. The key requirement for the equations is a smoothing property of the deterministic evolution operator which is typical in parabolic type problems. We show that if one has access to nonsmooth data estimates for the deterministic error operator together with its derivative of a space discretization procedure, then one obtains error estimates in pathwise Hölder norms with rates that can be read off the deterministic error rates. We illustrate the main result by considering a class of stochastic fractional order partial differential equations and space approximations performed by spectral Galerkin methods and finite elements. We also improve an existing result on the stochastic heat equation.","PeriodicalId":74872,"journal":{"name":"Stochastic partial differential equations : analysis and computations","volume":"11 3","pages":"1044-1088"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10404214/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9945355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Well-posedness for a stochastic 2D Euler equation with transport noise. 含传输噪声的随机二维Euler方程的适定性。

Stochastic partial differential equations : analysis and computations Pub Date : 2023-01-01 Epub Date: 2022-01-29 DOI: 10.1007/s40072-021-00233-7

Oana Lang, Dan Crisan

引用次数: 24

The hyperbolic Anderson model: moment estimates of the Malliavin derivatives and applications. 双曲安德森模型:马利文导数的矩估计及其应用。

Stochastic partial differential equations : analysis and computations Pub Date : 2022-01-01 Epub Date: 2022-01-18 DOI: 10.1007/s40072-021-00227-5

Raluca M Balan, David Nualart, Lluís Quer-Sardanyons, Guangqu Zheng

{"title":"The hyperbolic Anderson model: moment estimates of the Malliavin derivatives and applications.","authors":"Raluca M Balan, David Nualart, Lluís Quer-Sardanyons, Guangqu Zheng","doi":"10.1007/s40072-021-00227-5","DOIUrl":"https://doi.org/10.1007/s40072-021-00227-5","url":null,"abstract":"In this article, we study the hyperbolic Anderson model driven by a space-time colored Gaussian homogeneous noise with spatial dimension <math><mrow><mi>d</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn></mrow> </math> . Under mild assumptions, we provide <math><msup><mi>L</mi> <mi>p</mi></msup> </math> -estimates of the iterated Malliavin derivative of the solution in terms of the fundamental solution of the wave solution. To achieve this goal, we rely heavily on the Wiener chaos expansion of the solution. Our first application are quantitative central limit theorems for spatial averages of the solution to the hyperbolic Anderson model, where the rates of convergence are described by the total variation distance. These quantitative results have been elusive so far due to the temporal correlation of the noise blocking us from using the Itô calculus. A novel ingredient to overcome this difficulty is the second-order Gaussian Poincaré inequality coupled with the application of the aforementioned <math><msup><mi>L</mi> <mi>p</mi></msup> </math> -estimates of the first two Malliavin derivatives. Besides, we provide the corresponding functional central limit theorems. As a second application, we establish the absolute continuity of the law for the hyperbolic Anderson model. The <math><msup><mi>L</mi> <mi>p</mi></msup> </math> -estimates of Malliavin derivatives are crucial ingredients to verify a local version of Bouleau-Hirsch criterion for absolute continuity. Our approach substantially simplifies the arguments for the one-dimensional case, which has been studied in the recent work by [2].","PeriodicalId":74872,"journal":{"name":"Stochastic partial differential equations : analysis and computations","volume":"10 3","pages":"757-827"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9525444/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33488593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 13

Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM. 随机域上椭圆型问题的有限元与边界元耦合多水平求积分。

Stochastic partial differential equations : analysis and computations Pub Date : 2022-01-01 Epub Date: 2021-10-13 DOI: 10.1007/s40072-021-00214-w

Helmut Harbrecht, Marc Schmidlin

{"title":"Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM.","authors":"Helmut Harbrecht, Marc Schmidlin","doi":"10.1007/s40072-021-00214-w","DOIUrl":"https://doi.org/10.1007/s40072-021-00214-w","url":null,"abstract":"Elliptic boundary value problems which are posed on a random domain can be mapped to a fixed, nominal domain. The randomness is thus transferred to the diffusion matrix and the loading. While this domain mapping method is quite efficient for theory and practice, since only a single domain discretisation is needed, it also requires the knowledge of the domain mapping. However, in certain applications, the random domain is only described by its random boundary, while the quantity of interest is defined on a fixed, deterministic subdomain. In this setting, it thus becomes necessary to compute a random domain mapping on the whole domain, such that the domain mapping is the identity on the fixed subdomain and maps the boundary of the chosen fixed, nominal domain on to the random boundary. To overcome the necessity of computing such a mapping, we therefore couple the finite element method on the fixed subdomain with the boundary element method on the random boundary. We verify on one hand the regularity of the solution with respect to the random domain mapping required for many multilevel quadrature methods, such as the multilevel quasi-Monte Carlo quadrature using Halton points, the multilevel sparse anisotropic Gauss-Legendre and Clenshaw-Curtis quadratures and multilevel interlaced polynomial lattice rules. On the other hand, we derive the coupling formulation and show by numerical results that the approach is feasible.","PeriodicalId":74872,"journal":{"name":"Stochastic partial differential equations : analysis and computations","volume":"10 4","pages":"1619-1650"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9617976/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40443685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval. 随机半线性演化方程在极大区间上的动态低秩逼近的存在性。

Stochastic partial differential equations : analysis and computations Pub Date : 2021-01-01 Epub Date: 2020-08-05 DOI: 10.1007/s40072-020-00177-4

Yoshihito Kazashi, Fabio Nobile

引用次数: 6

An order approach to SPDEs with antimonotone terms. 具有反单调项的spde的一种有序方法。

Stochastic partial differential equations : analysis and computations Pub Date : 2020-01-01 Epub Date: 2020-01-03 DOI: 10.1007/s40072-019-00161-7

Luca Scarpa, Ulisse Stefanelli

引用次数: 0