can someone explain me in simpler way of what this paper has conveyed
$begingroup$
I do not have a thorough knowledge of measure-theoretic probability and Markov chain but I would start to learn by myself soon, but for few research-related works, I have to understand the theme of this paper. It would be a great help if someone explain me in a simple way what the paper has conveyed.
Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities M. F. BARNSLEY (), S. G. DEMKO, J. H. ELTON () and J. S. GERONIMO (**) School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332
http://www.numdam.org/article/AIHPB_1988__24_3_367_0.pdf
markov-chains contraction-operator
asked Dec 5 '18 at 15:37
MarkovMarkov
17.3k1059180
$endgroup$
add a comment |
$begingroup$
I do not have a thorough knowledge of measure-theoretic probability and Markov chain but I would start to learn by myself soon, but for few research-related works, I have to understand the theme of this paper. It would be a great help if someone explain me in a simple way what the paper has conveyed.
Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities M. F. BARNSLEY (), S. G. DEMKO, J. H. ELTON () and J. S. GERONIMO (**) School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332
http://www.numdam.org/article/AIHPB_1988__24_3_367_0.pdf
markov-chains contraction-operator
asked Dec 5 '18 at 15:37
MarkovMarkov
17.3k1059180
$endgroup$
add a comment |
$begingroup$
I do not have a thorough knowledge of measure-theoretic probability and Markov chain but I would start to learn by myself soon, but for few research-related works, I have to understand the theme of this paper. It would be a great help if someone explain me in a simple way what the paper has conveyed.
Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities M. F. BARNSLEY (), S. G. DEMKO, J. H. ELTON () and J. S. GERONIMO (**) School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332
http://www.numdam.org/article/AIHPB_1988__24_3_367_0.pdf
markov-chains contraction-operator
asked Dec 5 '18 at 15:37
MarkovMarkov
17.3k1059180
$endgroup$
I do not have a thorough knowledge of measure-theoretic probability and Markov chain but I would start to learn by myself soon, but for few research-related works, I have to understand the theme of this paper. It would be a great help if someone explain me in a simple way what the paper has conveyed.
Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities M. F. BARNSLEY (), S. G. DEMKO, J. H. ELTON () and J. S. GERONIMO (**) School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332
http://www.numdam.org/article/AIHPB_1988__24_3_367_0.pdf
markov-chains contraction-operator
markov-chains contraction-operator
asked Dec 5 '18 at 15:37
MarkovMarkov
17.3k1059180
asked Dec 5 '18 at 15:37
MarkovMarkov
17.3k1059180
edited Dec 5 '18 at 15:55
Markov
asked Dec 5 '18 at 15:37
MarkovMarkov
17.3k1059180
asked Dec 5 '18 at 15:37
MarkovMarkov
17.3k1059180
asked Dec 5 '18 at 15:37
MarkovMarkov
17.3k1059180
17.3k1059180
add a comment |
add a comment |
1 Answer
1
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oldest
votes
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A meta answer: this paper is both technical and fairly old, so if you are planning on using its results in your own research, you should keep in mind the possibility that there there have been improvements on the results in the past 30 years.
Several years ago I tried to see if I could use its results in a paper of mine. I found (1) that it was hard checking its hypotheses in my problem situation, and (2) it turned out its contractivity assumptions did not hold in my problem after all.
What you might want to do is read it in conjunction with Meyn and Tweedie's book on Markov chains, and translate the former into the latter's language as you go.
answered Dec 5 '18 at 16:31
kimchi loverkimchi lover
11k31128
$endgroup$
$begingroup$
The book you mention has 624 page..can you tell me which are portion I should take a deeper look?
$endgroup$
– Markov
Dec 5 '18 at 16:42
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(+1) A canonical entry into this mathematical domain is the review Iterated random functions by Persi Diaconis and David Freedman (from around 1998, I believe).
$endgroup$
– Did
Dec 5 '18 at 16:44
$begingroup$
Yes, M&T is long, and alas not very well organized. But it is a standard text, and you do want to learn the subject. On the narrower topic of IFS: I agree with Dld's advice.
$endgroup$
– kimchi lover
Dec 5 '18 at 16:49
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
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active
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active
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votes
$begingroup$
A meta answer: this paper is both technical and fairly old, so if you are planning on using its results in your own research, you should keep in mind the possibility that there there have been improvements on the results in the past 30 years.
Several years ago I tried to see if I could use its results in a paper of mine. I found (1) that it was hard checking its hypotheses in my problem situation, and (2) it turned out its contractivity assumptions did not hold in my problem after all.
What you might want to do is read it in conjunction with Meyn and Tweedie's book on Markov chains, and translate the former into the latter's language as you go.
answered Dec 5 '18 at 16:31
kimchi loverkimchi lover
11k31128
$endgroup$
$begingroup$
The book you mention has 624 page..can you tell me which are portion I should take a deeper look?
$endgroup$
– Markov
Dec 5 '18 at 16:42
$begingroup$
(+1) A canonical entry into this mathematical domain is the review Iterated random functions by Persi Diaconis and David Freedman (from around 1998, I believe).
$endgroup$
– Did
Dec 5 '18 at 16:44
$begingroup$
Yes, M&T is long, and alas not very well organized. But it is a standard text, and you do want to learn the subject. On the narrower topic of IFS: I agree with Dld's advice.
$endgroup$
– kimchi lover
Dec 5 '18 at 16:49
add a comment |
$begingroup$
A meta answer: this paper is both technical and fairly old, so if you are planning on using its results in your own research, you should keep in mind the possibility that there there have been improvements on the results in the past 30 years.
Several years ago I tried to see if I could use its results in a paper of mine. I found (1) that it was hard checking its hypotheses in my problem situation, and (2) it turned out its contractivity assumptions did not hold in my problem after all.
What you might want to do is read it in conjunction with Meyn and Tweedie's book on Markov chains, and translate the former into the latter's language as you go.
answered Dec 5 '18 at 16:31
kimchi loverkimchi lover
11k31128
$endgroup$
$begingroup$
The book you mention has 624 page..can you tell me which are portion I should take a deeper look?
$endgroup$
– Markov
Dec 5 '18 at 16:42
$begingroup$
(+1) A canonical entry into this mathematical domain is the review Iterated random functions by Persi Diaconis and David Freedman (from around 1998, I believe).
$endgroup$
– Did
Dec 5 '18 at 16:44
$begingroup$
Yes, M&T is long, and alas not very well organized. But it is a standard text, and you do want to learn the subject. On the narrower topic of IFS: I agree with Dld's advice.
$endgroup$
– kimchi lover
Dec 5 '18 at 16:49
add a comment |
$begingroup$
A meta answer: this paper is both technical and fairly old, so if you are planning on using its results in your own research, you should keep in mind the possibility that there there have been improvements on the results in the past 30 years.
Several years ago I tried to see if I could use its results in a paper of mine. I found (1) that it was hard checking its hypotheses in my problem situation, and (2) it turned out its contractivity assumptions did not hold in my problem after all.
What you might want to do is read it in conjunction with Meyn and Tweedie's book on Markov chains, and translate the former into the latter's language as you go.
answered Dec 5 '18 at 16:31
kimchi loverkimchi lover
11k31128
$endgroup$
A meta answer: this paper is both technical and fairly old, so if you are planning on using its results in your own research, you should keep in mind the possibility that there there have been improvements on the results in the past 30 years.
Several years ago I tried to see if I could use its results in a paper of mine. I found (1) that it was hard checking its hypotheses in my problem situation, and (2) it turned out its contractivity assumptions did not hold in my problem after all.
What you might want to do is read it in conjunction with Meyn and Tweedie's book on Markov chains, and translate the former into the latter's language as you go.
answered Dec 5 '18 at 16:31
kimchi loverkimchi lover
11k31128
answered Dec 5 '18 at 16:31
kimchi loverkimchi lover
11k31128
answered Dec 5 '18 at 16:31
kimchi loverkimchi lover
11k31128
answered Dec 5 '18 at 16:31
kimchi loverkimchi lover
11k31128
11k31128
$begingroup$
The book you mention has 624 page..can you tell me which are portion I should take a deeper look?
$endgroup$
– Markov
Dec 5 '18 at 16:42
$begingroup$
(+1) A canonical entry into this mathematical domain is the review Iterated random functions by Persi Diaconis and David Freedman (from around 1998, I believe).
$endgroup$
– Did
Dec 5 '18 at 16:44
$begingroup$
Yes, M&T is long, and alas not very well organized. But it is a standard text, and you do want to learn the subject. On the narrower topic of IFS: I agree with Dld's advice.
$endgroup$
– kimchi lover
Dec 5 '18 at 16:49
add a comment |
$begingroup$
The book you mention has 624 page..can you tell me which are portion I should take a deeper look?
$endgroup$
– Markov
Dec 5 '18 at 16:42
$begingroup$
(+1) A canonical entry into this mathematical domain is the review Iterated random functions by Persi Diaconis and David Freedman (from around 1998, I believe).
$endgroup$
– Did
Dec 5 '18 at 16:44
$begingroup$
Yes, M&T is long, and alas not very well organized. But it is a standard text, and you do want to learn the subject. On the narrower topic of IFS: I agree with Dld's advice.
$endgroup$
– kimchi lover
Dec 5 '18 at 16:49
$begingroup$
The book you mention has 624 page..can you tell me which are portion I should take a deeper look?
$endgroup$
– Markov
Dec 5 '18 at 16:42
$begingroup$
The book you mention has 624 page..can you tell me which are portion I should take a deeper look?
$endgroup$
– Markov
Dec 5 '18 at 16:42
$begingroup$
(+1) A canonical entry into this mathematical domain is the review Iterated random functions by Persi Diaconis and David Freedman (from around 1998, I believe).
$endgroup$
– Did
Dec 5 '18 at 16:44
$begingroup$
(+1) A canonical entry into this mathematical domain is the review Iterated random functions by Persi Diaconis and David Freedman (from around 1998, I believe).
$endgroup$
– Did
Dec 5 '18 at 16:44
$begingroup$
Yes, M&T is long, and alas not very well organized. But it is a standard text, and you do want to learn the subject. On the narrower topic of IFS: I agree with Dld's advice.
$endgroup$
– kimchi lover
Dec 5 '18 at 16:49
$begingroup$
Yes, M&T is long, and alas not very well organized. But it is a standard text, and you do want to learn the subject. On the narrower topic of IFS: I agree with Dld's advice.
$endgroup$
– kimchi lover
Dec 5 '18 at 16:49
add a comment |
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