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Why Martingales are so important?
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I'm studing probability, an I can see martingale everywhere. I can work with them, but I don't really see in what they are so important everywhere.
I know that $M_n$ is a martingale wrt the filtration $mathcal F_n$ if $M_n$ is $mathcal F_n-$measurable and if $$mathbb E[M_n+1mid mathcal F_n]=M_n.$$
In what this definition makes them so important ? And why are they everywhere ?
probability-theory martingales
asked Aug 2 at 8:28
user380364
808213
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up vote
2
down vote
favorite
I'm studing probability, an I can see martingale everywhere. I can work with them, but I don't really see in what they are so important everywhere.
I know that $M_n$ is a martingale wrt the filtration $mathcal F_n$ if $M_n$ is $mathcal F_n-$measurable and if $$mathbb E[M_n+1mid mathcal F_n]=M_n.$$
In what this definition makes them so important ? And why are they everywhere ?
probability-theory martingales
asked Aug 2 at 8:28
user380364
808213
5
Do you know how martingales originated? They came from gambling. They are models for what you call 'fair games'. However, they eventually became a powerful tool for proving theorems in Probability Theory. One of the nicest almost sure convergence theorems in Probability Theory is the Martingale Convergence Theorem.
– Kavi Rama Murthy
Aug 2 at 8:40
See here: math.stackexchange.com/questions/908908/…
– Math1000
Aug 2 at 13:06
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I'm studing probability, an I can see martingale everywhere. I can work with them, but I don't really see in what they are so important everywhere.
I know that $M_n$ is a martingale wrt the filtration $mathcal F_n$ if $M_n$ is $mathcal F_n-$measurable and if $$mathbb E[M_n+1mid mathcal F_n]=M_n.$$
In what this definition makes them so important ? And why are they everywhere ?
probability-theory martingales
asked Aug 2 at 8:28
user380364
808213
I'm studing probability, an I can see martingale everywhere. I can work with them, but I don't really see in what they are so important everywhere.
I know that $M_n$ is a martingale wrt the filtration $mathcal F_n$ if $M_n$ is $mathcal F_n-$measurable and if $$mathbb E[M_n+1mid mathcal F_n]=M_n.$$
In what this definition makes them so important ? And why are they everywhere ?
probability-theory martingales
asked Aug 2 at 8:28
user380364
808213
edited Aug 2 at 13:05
user223391
asked Aug 2 at 8:28
user380364
808213
asked Aug 2 at 8:28
user380364
808213
asked Aug 2 at 8:28
user380364
808213
808213
5
Do you know how martingales originated? They came from gambling. They are models for what you call 'fair games'. However, they eventually became a powerful tool for proving theorems in Probability Theory. One of the nicest almost sure convergence theorems in Probability Theory is the Martingale Convergence Theorem.
– Kavi Rama Murthy
Aug 2 at 8:40
See here: math.stackexchange.com/questions/908908/…
– Math1000
Aug 2 at 13:06
add a comment |Â
5
Do you know how martingales originated? They came from gambling. They are models for what you call 'fair games'. However, they eventually became a powerful tool for proving theorems in Probability Theory. One of the nicest almost sure convergence theorems in Probability Theory is the Martingale Convergence Theorem.
– Kavi Rama Murthy
Aug 2 at 8:40
See here: math.stackexchange.com/questions/908908/…
– Math1000
Aug 2 at 13:06
5
5
Do you know how martingales originated? They came from gambling. They are models for what you call 'fair games'. However, they eventually became a powerful tool for proving theorems in Probability Theory. One of the nicest almost sure convergence theorems in Probability Theory is the Martingale Convergence Theorem.
– Kavi Rama Murthy
Aug 2 at 8:40
Do you know how martingales originated? They came from gambling. They are models for what you call 'fair games'. However, they eventually became a powerful tool for proving theorems in Probability Theory. One of the nicest almost sure convergence theorems in Probability Theory is the Martingale Convergence Theorem.
– Kavi Rama Murthy
Aug 2 at 8:40
See here: math.stackexchange.com/questions/908908/…
– Math1000
Aug 2 at 13:06
See here: math.stackexchange.com/questions/908908/…
– Math1000
Aug 2 at 13:06
add a comment |Â
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5
Do you know how martingales originated? They came from gambling. They are models for what you call 'fair games'. However, they eventually became a powerful tool for proving theorems in Probability Theory. One of the nicest almost sure convergence theorems in Probability Theory is the Martingale Convergence Theorem.
– Kavi Rama Murthy
Aug 2 at 8:40
See here: math.stackexchange.com/questions/908908/…
– Math1000
Aug 2 at 13:06