Zobrazeno 1 - 10
of 164
pro vyhledávání: '"Davar Khoshnevisan"'
Publikováno v:
Stochastics and Partial Differential Equations: Analysis and Computations. 11:122-176
Suppose that $$\{u(t, x)\}_{t >0, x \in {\mathbb {R}}^d}$$ is the solution to a d-dimensional stochastic heat equation driven by a Gaussian noise that is white in time and has a spatially homogeneous covariance that satisfies Dalang’s condition. Th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f7a99f2530e58abcc0ad7e3ac2973bf0
https://doi.org/10.1007/s40072-021-00224-8
https://doi.org/10.1007/s40072-021-00224-8
Publikováno v:
SIAM Journal on Mathematical Analysis. 53:2084-2133
Suppose that $\{u(t\,, x)\}_{t >0, x \in\mathbb{R}^d}$ is the solution to a $d$-dimensional parabolic Anderson model with delta initial condition and driven by a Gaussian noise that is white in time and has a spatially homogeneous covariance given by
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5144f39214ae92148b089d5321b992e5
https://doi.org/10.1137/20m1350418
https://doi.org/10.1137/20m1350418
Publikováno v:
Electronic Journal of Probability. 26
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7f2d9d64321228adf48c690f3021d7d7
https://doi.org/10.1214/21-ejp690
https://doi.org/10.1214/21-ejp690
Let $\{u(t\,, x)\}_{t >0, x \in\mathbb{R}}$ denote the solution to the parabolic Anderson model with initial condition $\delta_0$ and driven by space-time white noise on $\mathbb{R}_+\times\mathbb{R}$, and let $p_t(x):= (2\pi t)^{-1/2}\exp\{-x^2/(2t)
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::17a97cc51d1b62bcc0ca799cadfd6b22
We present a central limit theorem for stationary random fields that are short-range dependent and asymptotically independent. As an application, we present a central limit theorem for an infinite family of interacting Itô-type diffusion processes.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::019c1f7ed104a75b203988a51a722911
Autor:
Davar Khoshnevisan, Edward C. Waymire
Publikováno v:
Notices of the American Mathematical Society. 64:616-619
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2c1623e83d6b77f6c9ada458282b8a81
https://doi.org/10.1090/noti1533
https://doi.org/10.1090/noti1533
Publikováno v:
Ann. Probab. 47, no. 1 (2019), 519-559
Let xi(t, x) denote space-time white noise and consider a reaction-diffusion equation of the form
(t, x) = 1/2u ''(t, x) + b(u(t, x)) + sigma(u(t,x))xi(t,x)
on R+ x [0, 1], with homogeneous Dirichlet boundary conditions and suitable initial
(t, x) = 1/2u ''(t, x) + b(u(t, x)) + sigma(u(t,x))xi(t,x)
on R+ x [0, 1], with homogeneous Dirichlet boundary conditions and suitable initial
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::746353ea45583f5ddb907f5ca38d3e3d
https://projecteuclid.org/euclid.aop/1544691627
https://projecteuclid.org/euclid.aop/1544691627
The study of intermittency for the parabolic Anderson problem usually focuses on the moments of the solution which can describe the high peaks in the probability space. In this paper we set up the equation on a finite spatial interval, and study the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1fee43e1a497877ec48a61dc13a50b3c
http://arxiv.org/abs/1808.06877
http://arxiv.org/abs/1808.06877
Publikováno v:
Electron. J. Probab.
We find formulas for the macroscopic Minkowski and Hausdorff dimensions of the range of an arbitrary transient walk in Z^d. This endeavor solves a problem of Barlow and Taylor (1991).
Comment: 37 pages, 5 figures
Comment: 37 pages, 5 figures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::547045e40262c3ed5c018835334f8b98
https://doi.org/10.1214/18-ejp201
https://doi.org/10.1214/18-ejp201
Publikováno v:
Stochastic Partial Differential Equations: Analysis and Computations. 3:133-158
Consider the stochastic partial differential equation $\partial_t u = Lu+\sigma(u)\xi$, where $\xi$ denotes space-time white noise and $L:=-(-\Delta)^{\alpha/2}$ denotes the fractional Laplace operator of index $\alpha/2\in(\nicefrac12\,,1]$. We stud
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e5316927898f4f12ced965c3bb2f8933
https://doi.org/10.1007/s40072-015-0045-y
https://doi.org/10.1007/s40072-015-0045-y