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Prerequisites to reading *Convergence of Probability Measures* by Patrick Billingsley.

3

1

$begingroup$

I want to improve myself in asymptotic theory regarding the realm of probability.

I tried reading Convergence of Probability Measures by Patrick Billingsley but right off the bat the De Moivre-Laplace limit theorem is mentioned. I have yet to prove this theorem.

So I was wondering if there was a text recommended to read before approaching Convergence of Probability Measures by Patrick Billingsley?

probability-theory reference-request asymptotics book-recommendation

share|cite|improve this question

asked May 3 '15 at 22:21

MonoliteMonolite

1,5922926

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add a comment | 

3

1

$begingroup$

I want to improve myself in asymptotic theory regarding the realm of probability.

I tried reading Convergence of Probability Measures by Patrick Billingsley but right off the bat the De Moivre-Laplace limit theorem is mentioned. I have yet to prove this theorem.

So I was wondering if there was a text recommended to read before approaching Convergence of Probability Measures by Patrick Billingsley?

probability-theory reference-request asymptotics book-recommendation

share|cite|improve this question

asked May 3 '15 at 22:21

MonoliteMonolite

1,5922926

$endgroup$

add a comment | 

$begingroup$

I want to improve myself in asymptotic theory regarding the realm of probability.

I tried reading Convergence of Probability Measures by Patrick Billingsley but right off the bat the De Moivre-Laplace limit theorem is mentioned. I have yet to prove this theorem.

So I was wondering if there was a text recommended to read before approaching Convergence of Probability Measures by Patrick Billingsley?

probability-theory reference-request asymptotics book-recommendation

share|cite|improve this question

asked May 3 '15 at 22:21

MonoliteMonolite

1,5922926

$endgroup$

share|cite|improve this question

asked May 3 '15 at 22:21

MonoliteMonolite

1,5922926

share|cite|improve this question

asked May 3 '15 at 22:21

MonoliteMonolite

1,5922926

asked May 3 '15 at 22:21

MonoliteMonolite

1,5922926

asked May 3 '15 at 22:21

MonoliteMonolite

1,5922926

2 Answers
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A course on graduate real analysis (e.g. Rudin Complex and Real analysis) and graduate probability (e.g. Billingsley's other book probability and measure) should be pretty solid. Actually probability and measure alone might be just good enough assuming some preparation on general topology, various "spaces" (Hilbert, Lp space in particular), Fourier analysis etc. A course on functional analysis (e.g. Rudin) is recommended but not necessary.

share|cite|improve this answer

answered Mar 22 at 20:29

Daniel LiDaniel Li

787414

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0

$begingroup$

I recommend Rick Durrett's Probability: Theory and Examples, as another answer pointed out, Billingsley's other book Probability and measure is also great but the approach in the book is somewhat different(it starts with introduction to normal number).

share|cite|improve this answer

answered Apr 9 at 0:58

The RThe R

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0

$begingroup$

A course on graduate real analysis (e.g. Rudin Complex and Real analysis) and graduate probability (e.g. Billingsley's other book probability and measure) should be pretty solid. Actually probability and measure alone might be just good enough assuming some preparation on general topology, various "spaces" (Hilbert, Lp space in particular), Fourier analysis etc. A course on functional analysis (e.g. Rudin) is recommended but not necessary.

share|cite|improve this answer

answered Mar 22 at 20:29

Daniel LiDaniel Li

787414

$endgroup$

add a comment | 

0

$begingroup$

A course on graduate real analysis (e.g. Rudin Complex and Real analysis) and graduate probability (e.g. Billingsley's other book probability and measure) should be pretty solid. Actually probability and measure alone might be just good enough assuming some preparation on general topology, various "spaces" (Hilbert, Lp space in particular), Fourier analysis etc. A course on functional analysis (e.g. Rudin) is recommended but not necessary.

share|cite|improve this answer

answered Mar 22 at 20:29

Daniel LiDaniel Li

787414

$endgroup$

add a comment | 

$begingroup$

A course on graduate real analysis (e.g. Rudin Complex and Real analysis) and graduate probability (e.g. Billingsley's other book probability and measure) should be pretty solid. Actually probability and measure alone might be just good enough assuming some preparation on general topology, various "spaces" (Hilbert, Lp space in particular), Fourier analysis etc. A course on functional analysis (e.g. Rudin) is recommended but not necessary.

share|cite|improve this answer

answered Mar 22 at 20:29

Daniel LiDaniel Li

787414

$endgroup$

share|cite|improve this answer

answered Mar 22 at 20:29

Daniel LiDaniel Li

787414

answered Mar 22 at 20:29

Daniel LiDaniel Li

787414

answered Mar 22 at 20:29

Daniel LiDaniel Li

787414

0

$begingroup$

I recommend Rick Durrett's Probability: Theory and Examples, as another answer pointed out, Billingsley's other book Probability and measure is also great but the approach in the book is somewhat different(it starts with introduction to normal number).

share|cite|improve this answer

answered Apr 9 at 0:58

The RThe R

6710

$endgroup$

add a comment | 

0

$begingroup$

I recommend Rick Durrett's Probability: Theory and Examples, as another answer pointed out, Billingsley's other book Probability and measure is also great but the approach in the book is somewhat different(it starts with introduction to normal number).

share|cite|improve this answer

answered Apr 9 at 0:58

The RThe R

6710

$endgroup$

add a comment | 

$begingroup$

I recommend Rick Durrett's Probability: Theory and Examples, as another answer pointed out, Billingsley's other book Probability and measure is also great but the approach in the book is somewhat different(it starts with introduction to normal number).

share|cite|improve this answer

answered Apr 9 at 0:58

The RThe R

6710

$endgroup$

share|cite|improve this answer

answered Apr 9 at 0:58

The RThe R

6710

answered Apr 9 at 0:58

The RThe R

6710

answered Apr 9 at 0:58

The RThe R

6710