The Martingle as an Orthogonal Projection

2nd International Scientific Conference (Pure Sciences, Brilliant Creativity and Renewed Building)

Jumaa, Suha^1 ; Ebrahim, H.H.^1

Department of Mathematics, College of Computer Science and Mathematics, University of Tikrit, Iraq^1

关键词: Martingale difference;    Orthogonal projection;    Orthogonality;    Orthogonality relations;    Square integrable;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/571/1/012009/pdf
DOI  :  10.1088/1757-899X/571/1/012009

来源: IOP

【 摘 要 】

This paper studies martingale as an orthogonal projection. It is proved that martingale achieves infimum relation if and only if it satisfies orthogonality relation. It is also proved that orthogonal martingale in Hilbert space achieves minimum relation. It is observed that martingale differences are orthogonal in Hilbert space and martingale can be represented as the sum of orthogonal difference.