Representation of Strongly Stationary Stochastic Processes

1993 ◽  
Vol 60 (3) ◽  
pp. 689-694 ◽  
Author(s):  
M. Di Paola
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Linear Systems ◽  
Stationary Processes ◽  
Orthogonality Conditions ◽  
Probabilistic Characterization ◽  
Stationary Stochastic Processes ◽  
Fixed Order ◽  
Strongly Stationary

A generalization of the orthogonality conditions for a stochastic process to represent strongly stationary processes up to a fixed order is presented. The particular case of non-normal delta correlated processes, and the probabilistic characterization of linear systems subjected to strongly stationary stochastic processes are also discussed.

Some comments on spectral representations of non-stationary stochastic processes

1973 ◽  
Vol 10 (04) ◽  
pp. 881-885 ◽  
Author(s):  
H. Tong
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Stationary Stochastic Process ◽  
Sufficient Condition ◽  
Stationary Stochastic Processes ◽  
Spectral Representations ◽  
Oscillatory Processes

The first part of the paper gives a multitude of essentially different representations of a stationary stochastic process. The second part gives a sufficient condition for the sum of two oscillatory processes to be again oscillatory.

Characterization of stochastic processes by stochastic integrals

1983 ◽  
Vol 15 (1) ◽  
pp. 81-98 ◽  
Author(s):  
B. L. S. Prakasa Rao
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Recent Work ◽  
Stochastic Integrals ◽  
Stable Processes ◽  
Process With Independent Increments ◽  
Independent Increments

Let be a continuous homogeneous stochastic process with independent increments. A review of the recent work on the characterization of Wiener and stable processes and connected results through stochastic integrals is presented. No proofs are given but appropriate references are mentioned.

Characterization of stochastic processes by stochastic integrals

1983 ◽  
Vol 15 (01) ◽  
pp. 81-98 ◽  
Author(s):  
B. L. S. Prakasa Rao
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Recent Work ◽  
Stochastic Integrals ◽  
Stable Processes ◽  
Process With Independent Increments ◽  
Independent Increments

Letbe a continuous homogeneous stochastic process with independent increments. A review of the recent work on the characterization of Wiener and stable processes and connected results through stochastic integrals is presented. No proofs are given but appropriate references are mentioned.

Some comments on spectral representations of non-stationary stochastic processes

1973 ◽  
Vol 10 (4) ◽  
pp. 881-885 ◽  
Author(s):  
H. Tong
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Stationary Stochastic Process ◽  
Sufficient Condition ◽  
Stationary Stochastic Processes ◽  
Spectral Representations ◽  
Oscillatory Processes

The first part of the paper gives a multitude of essentially different representations of a stationary stochastic process. The second part gives a sufficient condition for the sum of two oscillatory processes to be again oscillatory.

scholarly journals The nested Sinkhorn divergence to learn the nested distance

2021 ◽  
Author(s):  
Alois Pichler ◽  
Michael Weinhardt
Keyword(s):  
Stochastic Process ◽  
Fixed Point ◽  
Stochastic Processes ◽  
Numerical Experiments ◽  
Wasserstein Distance ◽  
Iteration Algorithm ◽  
Computational Advantage ◽  
The Difference ◽  
Nested Distance

AbstractThe nested distance builds on the Wasserstein distance to quantify the difference of stochastic processes, including also the evolution of information modelled by filtrations. The Sinkhorn divergence is a relaxation of the Wasserstein distance, which can be computed considerably faster. For this reason we employ the Sinkhorn divergence and take advantage of the related (fixed point) iteration algorithm. Furthermore, we investigate the transition of the entropy throughout the stages of the stochastic process and provide an entropy-regularized nested distance formulation, including a characterization of its dual. Numerical experiments affirm the computational advantage and supremacy.

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