Maximally distributed random fields under sublinear expectation

TL;DR

This paper introduces a new class of random fields called maximally distributed fields under sublinear expectation, constructs associated white noise, and develops stochastic integrals without the usual adaptability assumption.

Contribution

It defines maximally distributed random fields under sublinear expectation and constructs their white noise, extending the theory to spatial and temporal-spatial cases with direct stochastic integral definitions.

Findings

Constructed spatial maximally distributed white noise.

Established stochastic integrals without adaptability assumptions.

Unified temporal-spatial maximal distribution framework.

Abstract

This paper focuses on the maximal distribution on sublinear expectation space and introduces a new type of random fields with the maximally distributed finite-dimensional distribution. The corresponding spatial maximally distributed white noise is constructed, which includes the temporal-spatial situation as a special case due to the symmetrical independence property of maximal distribution. In addition, the stochastic integrals with respect to the spatial or temporal-spatial maximally distributed white noises are established in a quite direct way without the usual assumption of adaptability for integrand.