Title :
Some distributional properties of the continuous wavelet transform of random processes
Author :
Averkamp, R. ; Houdré, C.
Author_Institution :
Inst. fur Math. Stochastik, Freiburg Univ., Germany
fDate :
5/1/1998 12:00:00 AM
Abstract :
Without finite moment conditions, some properties of random processes, such as stationarity and self-similarity, are characterized via corresponding properties of their wavelet transform. Anyone of these distributional properties of the wavelet transform characterizes the corresponding property of the increments of the random process, of order equal to the order of regularity of the analyzing wavelet. Extensions of these results to random fields are then indicated
Keywords :
random processes; signal processing; statistical analysis; wavelet transforms; analyzing wavelet regularity; continuous wavelet transform; distributional properties; finite moment conditions; identification; random fields; random processes; self-similarity; signal analysis; stationarity; wavelet transform; Continuous wavelet transforms; Discrete wavelet transforms; Linear systems; Mathematics; Polynomials; Random processes; Signal analysis; Stochastic processes; Wavelet analysis; Wavelet transforms;
Journal_Title :
Information Theory, IEEE Transactions on
