Spatial and temporal white noises under sublinear G-expectation  

作　　者：Xiaojun Ji Shige Peng 

机构地区：[1]School of Mathematics,Shandong University,Jinan 250100,China [2]Zhongtai Securities Institute for Financial Studies,Shandong University,Jinan 250100,China

出　　处：《Science China Mathematics》2020年第1期61-82,共22页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. L1624032)

摘　　要：Under the framework of sublinear expectation,we introduce a new type of G-Gaussian random fields,which contains a type of spatial white noise as a special case.Based on this result,we also introduce a spatial-temporal G-white noise.Different from the case of linear expectation,in which the probability measure needs to be known,under the uncertainty of probability measures,spatial white noises are intrinsically different from temporal cases.Under the framework of sublinear expectation,we introduce a new type of G-Gaussian random fields,which contains a type of spatial white noise as a special case.Based on this result,we also introduce a spatial-temporal G-white noise.Different from the case of linear expectation,in which the probability measure needs to be known,under the uncertainty of probability measures,spatial white noises are intrinsically different from temporal cases.

关 键 词：sublinear expectation G-Brownian motion G-Gaussian random field G-white noise spatial and temporal white noise 

分 类 号：O211.6[理学—概率论与数理统计]