Non-strong mixing autoregressive processes

1984 ◽  
Vol 21 (04) ◽  
pp. 930-934 ◽  
Author(s):  
Donald W. K. Andrews
Keyword(s):  
Direct Proof ◽  
Strong Mixing ◽  
Autoregressive Processes ◽  
Mixing Conditions ◽  
First Order ◽  
Insight Into

Certain first-order autoregressive processes are shown not to be strong mixing. A direct proof is given. This proof gives considerably more insight into the nature of the result than do proofs by contradiction. The result and proof help to clarify the relation between the autoregressive and strong mixing conditions.

Non-strong mixing autoregressive processes

1984 ◽  
Vol 21 (4) ◽  
pp. 930-934 ◽  
Author(s):  
Donald W. K. Andrews
Keyword(s):  
Direct Proof ◽  
Strong Mixing ◽  
Autoregressive Processes ◽  
Mixing Conditions ◽  
First Order ◽  
Insight Into

Certain first-order autoregressive processes are shown not to be strong mixing. A direct proof is given. This proof gives considerably more insight into the nature of the result than do proofs by contradiction. The result and proof help to clarify the relation between the autoregressive and strong mixing conditions.

On strong mixing and Leadbetter's D condition

1981 ◽  
Vol 18 (3) ◽  
pp. 764-769 ◽  
Author(s):  
Michael R. Chernick
Keyword(s):  
Markov Process ◽  
Limit Theorems ◽  
Markov Property ◽  
Strong Mixing ◽  
Stationary Processes ◽  
Sufficient Condition ◽  
Autoregressive Processes ◽  
First Order ◽  
Stationary Markov Process

Strong mixing is a condition which is often assumed to prove limit theorems for strictly stationary processes. Leadbetter's condition D(un) is used to prove limit theorems for maxima of stationary processes.A sufficient condition for strong mixing to hold is given for the case where the process satisfies a pth-order Markov property. This condition can be easy to check for when p is small. This point is illustrated by two examples of first-order autoregressive processes.The condition D(un) is shown to hold for any stationary Markov process.

On strong mixing and Leadbetter's D condition

1981 ◽  
Vol 18 (03) ◽  
pp. 764-769 ◽  
Author(s):  
Michael R. Chernick
Keyword(s):  
Markov Process ◽  
Limit Theorems ◽  
Markov Property ◽  
Strong Mixing ◽  
Stationary Processes ◽  
Sufficient Condition ◽  
Autoregressive Processes ◽  
First Order ◽  
Stationary Markov Process

Strong mixing is a condition which is often assumed to prove limit theorems for strictly stationary processes. Leadbetter's conditionD(un) is used to prove limit theorems for maxima of stationary processes.A sufficient condition for strong mixing to hold is given for the case where the process satisfies apth-order Markov property. This condition can be easy to check for whenpis small. This point is illustrated by two examples of first-order autoregressive processes.The conditionD(un) is shown to hold for any stationary Markov process.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

Relational Chase Procedures Interpreted as Resolution with Paramodulation1

1991 ◽  
Vol 15 (2) ◽  
pp. 123-138
Author(s):  
Joachim Biskup ◽  
Bernhard Convent
Keyword(s):  
Alternative Interpretation ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Problem ◽  
First Order ◽  
Inference Problems ◽  
The One ◽  
The Relationship ◽  
Theoretical Foundations ◽  
Insight Into

In this paper the relationship between dependency theory and first-order logic is explored in order to show how relational chase procedures (i.e., algorithms to decide inference problems for dependencies) can be interpreted as clever implementations of well known refutation procedures of first-order logic with resolution and paramodulation. On the one hand this alternative interpretation provides a deeper insight into the theoretical foundations of chase procedures, whereas on the other hand it makes available an already well established theory with a great amount of known results and techniques to be used for further investigations of the inference problem for dependencies. Our presentation is a detailed and careful elaboration of an idea formerly outlined by Grant and Jacobs which up to now seems to be disregarded by the database community although it definitely deserves more attention.

ON THE SPECTRAL MEASURES OF SOME WEAKLY STATIONARY SEQUENCES INVOLVING RANDOMLY SPACED OBSERVATIONS

2012 ◽  
Vol 12 (01) ◽  
pp. 1150004
Author(s):  
RICHARD C. BRADLEY
Keyword(s):  
Spectral Density ◽  
Density Function ◽  
Spectral Density Function ◽  
Strong Mixing ◽  
Spectral Measures ◽  
Mixing Conditions ◽  
Stationary Sequences ◽  
Second Moments ◽  
The Central Limit Theorem ◽  
Complex Valued

In an earlier paper by the author, as part of a construction of a counterexample to the central limit theorem under certain strong mixing conditions, a formula is given that shows, for strictly stationary sequences with mean zero and finite second moments and a continuous spectral density function, how that spectral density function changes if the observations in that strictly stationary sequence are "randomly spread out" in a particular way, with independent "nonnegative geometric" numbers of zeros inserted in between. In this paper, that formula will be generalized to the class of weakly stationary, mean zero, complex-valued random sequences, with arbitrary spectral measure.

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