Nearby Variables with Nearby Conditional Laws and a Strong Approximation Theorem for Hilbert Space Valued Martingales

1989 ◽  
Author(s):  
D. Monrad ◽  
W. Philipp
Keyword(s):  
Hilbert Space ◽  
Strong Approximation ◽  
Approximation Theorem ◽  
Strong Approximation Theorem ◽  
Conditional Laws

A strong approximation for some non-stationary complex Gaussian processes

1981 ◽  
Vol 18 (2) ◽  
pp. 390-402 ◽  
Author(s):  
Peter Breuer
Keyword(s):  
Rate Of Convergence ◽  
Gaussian Processes ◽  
Strong Approximation ◽  
Approximation Theorem ◽  
Explicit Rate ◽  
Complex Valued ◽  
Strong Approximation Theorem

A strong approximation theorem is proved for some non-stationary complex-valued Gaussian processes and an explicit rate of convergence is achieved. The result answers a problem raised by S. Csörgő.

scholarly journals Representations of quadratic forms and their application to Selberg’s zeta functions

1976 ◽  
Vol 63 ◽  
pp. 153-162 ◽  
Author(s):  
Yoshiyuki Kitaoka
Keyword(s):  
Quadratic Forms ◽  
Strong Approximation ◽  
Approximation Theorem ◽  
Zeta Functions ◽  
Algebraic Number Field ◽  
Case Representation ◽  
Local Problems ◽  
Condition Rank ◽  
Quadratic Lattices ◽  
Strong Approximation Theorem

Let M and L be quadratic lattices over the maximal order of an algebraic number field. In case of dealing with representations of M by L, they sometimes assume certain indefiniteness and the condition rank L-rank M ≥ 3. In this case, representation problems are reduced not to global but to local problems by virtue of the strong approximation theorem for rotations and of the fact that for regular quadratic spaces U, V over a non-archimedian local field there is an isometry from U to V if dim V — dim U ≥ 3.

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