Abstract:
We present an overview on random fields and introduce their important statistical characteristics such as spectral representations, anisotropy, self-similarity and other scaling properties. Important examples of random fields include Gaussian random fields with stationary increments, solutions to systems of stochastic partial differential equations (SPDEs), and random matrices with random field entries.
The sample functions of random fields may be rough (e.g., nowhere differentiable) or continuously differentiable. Tools from fractal geometry or differential topology are needed to study their geometric and probabilistic properties. We will provide some examples of these results for Gaussian random fields and the solutions to SPDEs.
2023-05-22 16:00 ~ 2023-05-22 17:00
Prof. Yimin Xiao (Michigan State University)
Room 201, General Building III