IEICE TRANSACTIONS on Fundamentals
Generating Stochastic Processes Based on the Finitary Interval Algorithm
Summary :
We point out that the interval algorithm can be expressed in the form of a shift on the sequence space. Then we clarify that, by using a Bernoulli process, the interval algorithm can generate only a block of Markov chains or a sequence of independent blocks of Markov chains but not a stationary Markov process. By virtue of the finitary coding constructed by Hamachi and Keane, we obtain the procedure, called the finitary interval algorithm, to generate a Markov process by using the interval algorithm. The finitary interval algorithm also gives maps, defined almost everywhere, which transform a Markov measure to a Bernoulli measure.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.9 pp.2482-2488
- Publication Date
- 2008/09/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e91-a.9.2482
- Type of Manuscript
- Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
- Category
- Communications and Sequences
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Keyword
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Hiroshi FUJISAKI, "Generating Stochastic Processes Based on the Finitary Interval Algorithm" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 9, pp. 2482-2488, September 2008, doi: 10.1093/ietfec/e91-a.9.2482.
Abstract: We point out that the interval algorithm can be expressed in the form of a shift on the sequence space. Then we clarify that, by using a Bernoulli process, the interval algorithm can generate only a block of Markov chains or a sequence of independent blocks of Markov chains but not a stationary Markov process. By virtue of the finitary coding constructed by Hamachi and Keane, we obtain the procedure, called the finitary interval algorithm, to generate a Markov process by using the interval algorithm. The finitary interval algorithm also gives maps, defined almost everywhere, which transform a Markov measure to a Bernoulli measure.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.9.2482/_p
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@ARTICLE{e91-a_9_2482,
author={Hiroshi FUJISAKI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Generating Stochastic Processes Based on the Finitary Interval Algorithm},
year={2008},
volume={E91-A},
number={9},
pages={2482-2488},
abstract={We point out that the interval algorithm can be expressed in the form of a shift on the sequence space. Then we clarify that, by using a Bernoulli process, the interval algorithm can generate only a block of Markov chains or a sequence of independent blocks of Markov chains but not a stationary Markov process. By virtue of the finitary coding constructed by Hamachi and Keane, we obtain the procedure, called the finitary interval algorithm, to generate a Markov process by using the interval algorithm. The finitary interval algorithm also gives maps, defined almost everywhere, which transform a Markov measure to a Bernoulli measure.},
keywords={},
doi={10.1093/ietfec/e91-a.9.2482},
ISSN={1745-1337},
month={September},}
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TY - JOUR
TI - Generating Stochastic Processes Based on the Finitary Interval Algorithm
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2482
EP - 2488
AU - Hiroshi FUJISAKI
PY - 2008
DO - 10.1093/ietfec/e91-a.9.2482
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E91-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2008
AB - We point out that the interval algorithm can be expressed in the form of a shift on the sequence space. Then we clarify that, by using a Bernoulli process, the interval algorithm can generate only a block of Markov chains or a sequence of independent blocks of Markov chains but not a stationary Markov process. By virtue of the finitary coding constructed by Hamachi and Keane, we obtain the procedure, called the finitary interval algorithm, to generate a Markov process by using the interval algorithm. The finitary interval algorithm also gives maps, defined almost everywhere, which transform a Markov measure to a Bernoulli measure.
ER -
English
