Coordinate changed random fields on manifolds

Abstract

We introduce a class of time dependent random fields on compact Riemannian monifolds. These are represented by time-changed Brownian motions. These processes are time-changed diffusion, or the stochastic solution to the equation involving the Laplace-Beltrami operator and a time-fractional derivative of order $\beta \in (0,1)$. The time dependent random fields we present in this work can therefore be realized through composition and can be viewed as random fields on randomly varying manifolds.

26 pages, submitted for publication

References in corpus (4)

• Fractional Cauchy problems on bounded domains
• Fractional diffusion equations and processes with randomly varying time
• Fractional Laplacian on the torus
• Dynamics of two topologically entangled chains

Cited by in corpus (5)

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• Fractional equations via convergence of forms
• Fractional gradient and its application to the fractional advection equation
• Isotropic covariance matrix functions on compact two-point homogeneous spaces
• Models of space-time random fields on the sphere