Stochastics and Partial Differential Equations-Analysis and Computations最新文献

Pathwise uniqueness for singular stochastic Volterra equations with Hölder coefficients 具有赫尔德系数的奇异随机 Volterra方程的路径唯一性

IF 1.5 3区数学

Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2024-08-14 DOI: 10.1007/s40072-024-00335-y

David J. Prömel, David Scheffels

引用次数: 0

BPHZ renormalisation and vanishing subcriticality asymptotics of the fractional $$Phi ^3_d$$ model 分数 $$Phi ^3_d$$ 模型的 BPHZ 重正化和消失次临界渐近性

IF 1.5 3区数学

Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2024-06-09 DOI: 10.1007/s40072-024-00331-2

Nils Berglund, Yvain Bruned

引用次数: 0

Long-term dynamics of fractional stochastic delay reaction–diffusion equations on unbounded domains 无界域上分数随机延迟反应-扩散方程的长期动力学

IF 1.5 3区数学

Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2024-06-07 DOI: 10.1007/s40072-024-00334-z

Zhang Chen, Bixiang Wang

引用次数: 0

Decay of correlations in stochastic quantization: the exponential Euclidean field in two dimensions 随机量化中的相关性衰减：二维指数欧氏场

IF 1.5 3区数学

Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2024-05-07 DOI: 10.1007/s40072-024-00328-x

Massimiliano Gubinelli, Martina Hofmanová, Nimit Rana

引用次数: 0

A weighted $$L_q(L_p)$$ -theory for fully degenerate second-order evolution equations with unbounded time-measurable coefficients 具有不可限时系数的完全退化二阶演化方程的加权 $$L_q(L_p)$$ 理论

IF 1.5 3区数学

Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2024-04-29 DOI: 10.1007/s40072-024-00330-3

Ildoo Kim

引用次数: 0

$$L_p$$ -solvability and Hölder regularity for stochastic time fractional Burgers’ equations driven by multiplicative space-time white noise 由乘法时空白噪声驱动的随机时分数布尔格斯方程的$L_p$$$可解性和霍尔德正则性

IF 1.5 3区数学

Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2024-04-27 DOI: 10.1007/s40072-024-00329-w

Beom-Seok Han

{"title":"$$L_p$$ -solvability and Hölder regularity for stochastic time fractional Burgers’ equations driven by multiplicative space-time white noise","authors":"Beom-Seok Han","doi":"10.1007/s40072-024-00329-w","DOIUrl":"https://doi.org/10.1007/s40072-024-00329-w","url":null,"abstract":"This paper establishes (L_p)-solvability for stochastic time fractional Burgers’ equations driven by multiplicative space-time white noise: $$begin{aligned} partial _t^alpha u = a^{ij}u_{x^ix^j} + b^{i}u_{x^i} + cu + {bar{b}}^i u u_{x^i} + partial _t^beta int _0^t sigma (u)dW_t,quad t>0;quad u(0,cdot ) = u_0, end{aligned}$$where (alpha in (0,1)), (beta < 3alpha /4+1/2), and (d< 4--2(2beta -1)_+/alpha ). The operators (partial _t^alpha ) and (partial _t^beta ) are the Caputo fractional derivatives of order (alpha ) and (beta ), respectively. The process (W_t) is an (L_2(mathbb {R}^d))-valued cylindrical Wiener process, and the coefficients (a^{ij}, b^i, c, {bar{b}}^{i}) and (sigma (u)) are random. In addition to the uniqueness and existence of a solution, the Hölder regularity of the solution is also established. For example, for any constant (T<infty ), small (varepsilon >0), and almost sure (omega in varOmega ), $$begin{aligned} sup _{xin mathbb {R}^d}|u(omega ,cdot ,x)|_{C^{left[ frac{alpha }{2}left( left( 2-(2beta -1)_+/alpha -d/2 right) wedge 1 right) +frac{(2beta -1)_{-}}{2} right] wedge 1-varepsilon }([0,T])}<infty end{aligned}$$and $$begin{aligned} sup _{tle T}|u(omega ,t,cdot )|_{C^{left( 2-(2beta -1)_+/alpha -d/2 right) wedge 1 - varepsilon }(mathbb {R}^d)} < infty . end{aligned}$$The Hölder regularity of the solution in time changes behavior at (beta = 1/2). Furthermore, if (beta ge 1/2), then the Hölder regularity of the solution in time is (alpha /2) times that in space.","PeriodicalId":48569,"journal":{"name":"Stochastics and Partial Differential Equations-Analysis and Computations","volume":"57 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140808765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Temporal fractal nature of linearized Kuramoto–Sivashinsky SPDEs and their gradient in one-to-three dimensions 线性化 Kuramoto-Sivashinsky SPDEs 的时间分形性质及其一至三维梯度

IF 1.5 3区数学

Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2024-03-21 DOI: 10.1007/s40072-024-00327-y

Wensheng Wang, Lu Yuan

{"title":"Temporal fractal nature of linearized Kuramoto–Sivashinsky SPDEs and their gradient in one-to-three dimensions","authors":"Wensheng Wang, Lu Yuan","doi":"10.1007/s40072-024-00327-y","DOIUrl":"https://doi.org/10.1007/s40072-024-00327-y","url":null,"abstract":"Let (U={U(t,x), (t,x)in mathring{{mathbb {R}}}_+times {mathbb {R}}^d}) and (partial _{x}U={partial _{x}U(t,x), (t,x)in mathring{{mathbb {R}}}_+times {mathbb {R}}}) be the solution and gradient solution of the fourth order linearized Kuramoto–Sivashinsky (L-KS) SPDE, driven by the space-time white noise in one-to-three dimensional spaces, respectively. We use the underlying explicit kernels to prove the exact global temporal moduli and temporal LILs for the L-KS SPDEs and gradient, and utilize them to prove that the sets of temporal fast points where exceptional oscillation of (U(cdot ,x)) and (partial _{x}U(cdot ,x)) occur infinitely often are random fractals, and evaluate their Hausdorff dimensions and their hitting probabilities. It has been confirmed that these points of (U(cdot ,x)) and (partial _{x}U(cdot ,x)), in time, are everywhere dense with power of the continuum almost surely, and their hitting probabilities are determined by the packing dimension (dim _{_{p}}(B)) of the target set B.","PeriodicalId":48569,"journal":{"name":"Stochastics and Partial Differential Equations-Analysis and Computations","volume":"220 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140196196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Weak error analysis for a nonlinear SPDE approximation of the Dean–Kawasaki equation 迪安-川崎方程的非线性 SPDE 近似的弱误差分析

IF 1.5 3区数学

Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2024-03-15 DOI: 10.1007/s40072-024-00324-1

Ana Djurdjevac, Helena Kremp, Nicolas Perkowski

引用次数: 0

Convergence of stratified MCMC sampling of non-reversible dynamics 非可逆动力学分层 MCMC 采样的收敛性

IF 1.5 3区数学

Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2024-03-01 DOI: 10.1007/s40072-024-00325-0

Gabriel Earle, Jonathan C. Mattingly

引用次数: 0

Regularity of random elliptic operators with degenerate coefficients and applications to stochastic homogenization 具有退化系数的随机椭圆算子的正则性及其在随机均质化中的应用

IF 1.5 3区数学

Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2024-02-27 DOI: 10.1007/s40072-023-00322-9

Peter Bella, Michael Kniely

{"title":"Regularity of random elliptic operators with degenerate coefficients and applications to stochastic homogenization","authors":"Peter Bella, Michael Kniely","doi":"10.1007/s40072-023-00322-9","DOIUrl":"https://doi.org/10.1007/s40072-023-00322-9","url":null,"abstract":"We consider degenerate elliptic equations of second order in divergence form with a symmetric random coefficient field a. Extending the work of Bella et al. (Ann Appl Probab 28(3):1379–1422, 2018), who established the large-scale (C^{1,alpha }) regularity of a-harmonic functions in a degenerate situation, we provide stretched exponential moments for the minimal radius (r_*) describing the minimal scale for this (C^{1,alpha }) regularity. As an application to stochastic homogenization, we partially generalize results by Gloria et al. (Anal PDE 14(8):2497–2537, 2021) on the growth of the corrector, the decay of its gradient, and a quantitative two-scale expansion to the degenerate setting. On a technical level, we demand the ensemble of coefficient fields to be stationary and subject to a spectral gap inequality, and we impose moment bounds on a and (a^{-1}). We also introduce the ellipticity radius (r_e) which encodes the minimal scale where these moments are close to their positive expectation value.\u0000","PeriodicalId":48569,"journal":{"name":"Stochastics and Partial Differential Equations-Analysis and Computations","volume":"11 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139980086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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