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Random partitions tending to identity
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The following is a doubt that I have about the definition of sequence of random partitions tending to the identity. What does the author mean by tending to the identity? It is obvious from the context that the author refers to a sequence of random partitions such that $lim_n to infty Vert sigma_n Vert = 0$, but tending to identity is not a clear and intuitive definition.
I would really appreciate if someone could help with the definition, please.
By the way:
$mathbbL$ is the space of adapted caglad processes
$mathbbD$ is the space of adapted cadlag processes
$S$ is the space of simple predictable processes
probability-theory stochastic-calculus stochastic-analysis
asked Jul 18 at 17:08
Ivan
587
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up vote
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The following is a doubt that I have about the definition of sequence of random partitions tending to the identity. What does the author mean by tending to the identity? It is obvious from the context that the author refers to a sequence of random partitions such that $lim_n to infty Vert sigma_n Vert = 0$, but tending to identity is not a clear and intuitive definition.
I would really appreciate if someone could help with the definition, please.
By the way:
$mathbbL$ is the space of adapted caglad processes
$mathbbD$ is the space of adapted cadlag processes
$S$ is the space of simple predictable processes
probability-theory stochastic-calculus stochastic-analysis
asked Jul 18 at 17:08
Ivan
587
2
The basic idea is that if the largest of the stopping times goes to infinity and greatest distance between them goes to zero, then a process sampled at the partition will look more and more like the original process, so the partition "tends to the identity" in the sense that the sampling operation it represents tends to the identity, i. e. sampling "at infinity" recovers the original process (obviously speaking non-rigorously).
– joriki
Jul 18 at 17:26
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
The following is a doubt that I have about the definition of sequence of random partitions tending to the identity. What does the author mean by tending to the identity? It is obvious from the context that the author refers to a sequence of random partitions such that $lim_n to infty Vert sigma_n Vert = 0$, but tending to identity is not a clear and intuitive definition.
I would really appreciate if someone could help with the definition, please.
By the way:
$mathbbL$ is the space of adapted caglad processes
$mathbbD$ is the space of adapted cadlag processes
$S$ is the space of simple predictable processes
probability-theory stochastic-calculus stochastic-analysis
asked Jul 18 at 17:08
Ivan
587
The following is a doubt that I have about the definition of sequence of random partitions tending to the identity. What does the author mean by tending to the identity? It is obvious from the context that the author refers to a sequence of random partitions such that $lim_n to infty Vert sigma_n Vert = 0$, but tending to identity is not a clear and intuitive definition.
I would really appreciate if someone could help with the definition, please.
By the way:
$mathbbL$ is the space of adapted caglad processes
$mathbbD$ is the space of adapted cadlag processes
$S$ is the space of simple predictable processes
probability-theory stochastic-calculus stochastic-analysis
asked Jul 18 at 17:08
Ivan
587
asked Jul 18 at 17:08
Ivan
587
asked Jul 18 at 17:08
Ivan
587
asked Jul 18 at 17:08
Ivan
587
587
2
The basic idea is that if the largest of the stopping times goes to infinity and greatest distance between them goes to zero, then a process sampled at the partition will look more and more like the original process, so the partition "tends to the identity" in the sense that the sampling operation it represents tends to the identity, i. e. sampling "at infinity" recovers the original process (obviously speaking non-rigorously).
– joriki
Jul 18 at 17:26
add a comment |Â
2
The basic idea is that if the largest of the stopping times goes to infinity and greatest distance between them goes to zero, then a process sampled at the partition will look more and more like the original process, so the partition "tends to the identity" in the sense that the sampling operation it represents tends to the identity, i. e. sampling "at infinity" recovers the original process (obviously speaking non-rigorously).
– joriki
Jul 18 at 17:26
2
2
The basic idea is that if the largest of the stopping times goes to infinity and greatest distance between them goes to zero, then a process sampled at the partition will look more and more like the original process, so the partition "tends to the identity" in the sense that the sampling operation it represents tends to the identity, i. e. sampling "at infinity" recovers the original process (obviously speaking non-rigorously).
– joriki
Jul 18 at 17:26
The basic idea is that if the largest of the stopping times goes to infinity and greatest distance between them goes to zero, then a process sampled at the partition will look more and more like the original process, so the partition "tends to the identity" in the sense that the sampling operation it represents tends to the identity, i. e. sampling "at infinity" recovers the original process (obviously speaking non-rigorously).
– joriki
Jul 18 at 17:26
add a comment |Â
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2
The basic idea is that if the largest of the stopping times goes to infinity and greatest distance between them goes to zero, then a process sampled at the partition will look more and more like the original process, so the partition "tends to the identity" in the sense that the sampling operation it represents tends to the identity, i. e. sampling "at infinity" recovers the original process (obviously speaking non-rigorously).
– joriki
Jul 18 at 17:26