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Maximally Distributed Random Fields under Sublinear Expectation

In: Stochastic Analysis, Filtering, and Stochastic Optimization

Author

Listed:
  • Xinpeng Li

    (Shandong University, Research Center for Mathematics and Interdisciplinary Sciences)

  • Shige Peng

    (Shandong University, School of Mathematics)

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.

Suggested Citation

  • Xinpeng Li & Shige Peng, 2022. "Maximally Distributed Random Fields under Sublinear Expectation," Springer Books, in: George Yin & Thaleia Zariphopoulou (ed.), Stochastic Analysis, Filtering, and Stochastic Optimization, pages 339-356, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98519-6_14
    DOI: 10.1007/978-3-030-98519-6_14
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