Let{X(m,n)}_(m,m=0,±1,±2…)be a stationary random field.The closed linearspace spanned by all X(m,n):m,n=0,±1,±2,…is denoted by L(X).Throughoutthe following pages L_1(x:s)will denote the subspace ...Let{X(m,n)}_(m,m=0,±1,±2…)be a stationary random field.The closed linearspace spanned by all X(m,n):m,n=0,±1,±2,…is denoted by L(X).Throughoutthe following pages L_1(x:s)will denote the subspace generated by all X(m,n):m≤s,-∞<n<∞;L_2(x:t)will denote the subspace generated by all X(m,n):-∞<m<∞,n≤t;and L_k(x:-∞)will denote the intersection L_k(x:s),(k=1,2).展开更多
In this paper, we consider the nonsymmetrical half-plane prediction. A prediction theoretic proofof the fundamental formula about one step prediction error is given. A Wold-type decomposition andits spectral represent...In this paper, we consider the nonsymmetrical half-plane prediction. A prediction theoretic proofof the fundamental formula about one step prediction error is given. A Wold-type decomposition andits spectral representation theorem are proved. Spectral extraction problems of the half-plane innova-tions and its singular components are investigated.展开更多
It is known that the strongly regular stationary random field possesses the following two properties: (ⅰ) The spectral measure is absolutely continuous w. r. t. the two-dimensional Lebesgue measure.
文摘Let{X(m,n)}_(m,m=0,±1,±2…)be a stationary random field.The closed linearspace spanned by all X(m,n):m,n=0,±1,±2,…is denoted by L(X).Throughoutthe following pages L_1(x:s)will denote the subspace generated by all X(m,n):m≤s,-∞<n<∞;L_2(x:t)will denote the subspace generated by all X(m,n):-∞<m<∞,n≤t;and L_k(x:-∞)will denote the intersection L_k(x:s),(k=1,2).
基金Research supported in part by the National Natural Science Fundation of China
文摘In this paper, we consider the nonsymmetrical half-plane prediction. A prediction theoretic proofof the fundamental formula about one step prediction error is given. A Wold-type decomposition andits spectral representation theorem are proved. Spectral extraction problems of the half-plane innova-tions and its singular components are investigated.
文摘It is known that the strongly regular stationary random field possesses the following two properties: (ⅰ) The spectral measure is absolutely continuous w. r. t. the two-dimensional Lebesgue measure.
