M-dependent-process
From Encyclopedia of Mathematics
A discrete-time stochastic process is
-dependent if for all
the joint stochastic variables
are independent of the joint stochastic variables
.
Such processes arise naturally as limits of rescaling transformations (renormalizations) and (hence) as examples of processes with scaling symmetries [a1]. Examples of -dependent processes are given by
-block factors. These are defined as follows. Let
be an independent process and
a function of
variables; let
; then the
-block factor
is an
-dependent process.
There are one-dependent processes which are not -block factors, [a2].
References
[a1] | G.L. O'Brien, "Scaling transformations for ![]() |
[a2] | J. Aaronson, D. Gilat, M. Keane, V. de Valk, "An algebraic construction of a class of one-dependent processes" Ann. Probab. , 17 (1988) pp. 128–143 |
[a3] | S. Janson, "Runs in ![]() |
[a4] | G. Haiman, "Valeurs extrémales de suites stationaires de variable aléatoires ![]() |
How to Cite This Entry:
M-dependent-process. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=M-dependent-process&oldid=14932
M-dependent-process. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=M-dependent-process&oldid=14932