Subordinated Gaussian random fields in elliptic partial differential equations

Isotropic Gaussian Random Fields on the Sphere: Regularity, Fast Simulation and Stochastic Partial Differential Equations

Isotropic Gaussian random fields on the sphere are characterized by Karhunen–Loève expansions with respect to the spherical harmonic functions and the angular power spectrum. The smoothness of the covariance is connected to the decay of the angular power spectrum and the relation to sample Hölder continuity and sample differentiability of the random fields is discussed. Rates of convergence of ...

NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET Multivariate Gaussian Random Fields Using Systems of Stochastic Partial Differential Equations

In this paper a new approach for constructing multivariate Gaussian random fields (GRFs) using systems of stochastic partial differential equations (SPDEs) has been introduced and applied to simulated data and real data. By solving a system of SPDEs, we can construct multivariate GRFs. On the theoretical side, the notorious requirement of non-negative definiteness for the covariance matrix of t...

Lecture Notes on Elliptic Partial Differential Equations

Essential Spectra of Elliptic Partial Differential Equations

Let A be a closed, densely defined operator in a Banach space X. There are several definitions of the "essential" spectrum of A (cf. [ l ] , [2]). According to Wolf [3], [4] it is the complement in the complex plane of the $-set of A. The $-set $A of A is the set of points X for which (a) a(A — X), the dimension of the null space of A — X, is finite (b) R(A —X), the range of A —X, is closed (c)...

Random fractional functional differential equations

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.