On the infinite divisibility of squared Gaussian processes
نویسندگان
چکیده
منابع مشابه
ON THE INFINITE ORDER MARKOV PROCESSES
The notion of infinite order Markov process is introduced and the Markov property of the flow of information is established.
متن کاملInfinite Divisibility of Gaussian Squares with Non–zero Means
Let η = (η1, . . . , ηn) be an R n valued Gaussian random variable and c = (c1, . . . , cn) a vector in R. We give necessary and sufficient conditions for ((η1 + c1α) , . . . , (ηn + cnα) ) to be infinitely divisible for all α ∈ R, and point out how this result is related to local times of Markov chains determined by the covariance matrix of η.
متن کاملBeyond Gaussian Processes: On the Distributions of Infinite Networks
A general analysis of the limiting distribution of neural network functions is performed, with emphasis on non-Gaussian limits. We show that with i.i.d. symmetric stable output weights, and more generally with weights distributed from the normal domain of attraction of a stable variable, that the neural functions converge in distribution to stable processes. Conditions are also investigated und...
متن کاملThe Rate of Entropy for Gaussian Processes
In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...
متن کاملGärtner-Ellis condition for squared asymptotically stationary Gaussian processes
The Gärtner-Ellis condition for the square of an asymptotically stationary Gaussian process is established. The same limit holds for the conditional distribution given any fixed initial point, which entails weak multiplicative ergodicity. The limit is shown to be the Laplace transform of a convolution of Gamma distributions with Poisson compound of exponentials. A proof based on WienerHopf fact...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2003
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-002-0245-z