Recursive Poisson Process?

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I would like to know if there is a name for a type of process that works as follows: Suppose we have a Poisson process with rate paramter $lambda$. At each new arrival at time $t$ of this process, a new sub-process begins, which is also Poisson with some new parameter $lambda_t$. This parameter can be deterministic or generated via some distribution. So this gives us many Possion processes that are running in parallel.



Is anything know about this type of process? Can it be described via one large Poisson process?




poisson-process




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    "a new sub-process begins, which is also Poisson with some new parameter λt, which can be deterministic or generated via some distribution" If Poisson, the subprocess cannot be deterministic. Likewise, please explain "generated via some distribution".
    – Did
    Jul 29 at 16:55






  • 1




    Sorry, I mean that the parameter $lambda_t$ may be deterministic or random, not the process.
    – theQman
    Jul 29 at 18:17















up vote
1
down vote

favorite












I would like to know if there is a name for a type of process that works as follows: Suppose we have a Poisson process with rate paramter $lambda$. At each new arrival at time $t$ of this process, a new sub-process begins, which is also Poisson with some new parameter $lambda_t$. This parameter can be deterministic or generated via some distribution. So this gives us many Possion processes that are running in parallel.



Is anything know about this type of process? Can it be described via one large Poisson process?




poisson-process




share|cite|improve this question

















  • 1




    "a new sub-process begins, which is also Poisson with some new parameter λt, which can be deterministic or generated via some distribution" If Poisson, the subprocess cannot be deterministic. Likewise, please explain "generated via some distribution".
    – Did
    Jul 29 at 16:55






  • 1




    Sorry, I mean that the parameter $lambda_t$ may be deterministic or random, not the process.
    – theQman
    Jul 29 at 18:17













up vote
1
down vote

favorite









up vote
1
down vote

favorite











I would like to know if there is a name for a type of process that works as follows: Suppose we have a Poisson process with rate paramter $lambda$. At each new arrival at time $t$ of this process, a new sub-process begins, which is also Poisson with some new parameter $lambda_t$. This parameter can be deterministic or generated via some distribution. So this gives us many Possion processes that are running in parallel.



Is anything know about this type of process? Can it be described via one large Poisson process?




poisson-process




share|cite|improve this question













I would like to know if there is a name for a type of process that works as follows: Suppose we have a Poisson process with rate paramter $lambda$. At each new arrival at time $t$ of this process, a new sub-process begins, which is also Poisson with some new parameter $lambda_t$. This parameter can be deterministic or generated via some distribution. So this gives us many Possion processes that are running in parallel.



Is anything know about this type of process? Can it be described via one large Poisson process?





poisson-process





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 29 at 20:23
























asked Jul 29 at 16:32









theQman

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39218







  • 1




    "a new sub-process begins, which is also Poisson with some new parameter λt, which can be deterministic or generated via some distribution" If Poisson, the subprocess cannot be deterministic. Likewise, please explain "generated via some distribution".
    – Did
    Jul 29 at 16:55






  • 1




    Sorry, I mean that the parameter $lambda_t$ may be deterministic or random, not the process.
    – theQman
    Jul 29 at 18:17













  • 1




    "a new sub-process begins, which is also Poisson with some new parameter λt, which can be deterministic or generated via some distribution" If Poisson, the subprocess cannot be deterministic. Likewise, please explain "generated via some distribution".
    – Did
    Jul 29 at 16:55






  • 1




    Sorry, I mean that the parameter $lambda_t$ may be deterministic or random, not the process.
    – theQman
    Jul 29 at 18:17








1




1




"a new sub-process begins, which is also Poisson with some new parameter λt, which can be deterministic or generated via some distribution" If Poisson, the subprocess cannot be deterministic. Likewise, please explain "generated via some distribution".
– Did
Jul 29 at 16:55




"a new sub-process begins, which is also Poisson with some new parameter λt, which can be deterministic or generated via some distribution" If Poisson, the subprocess cannot be deterministic. Likewise, please explain "generated via some distribution".
– Did
Jul 29 at 16:55




1




1




Sorry, I mean that the parameter $lambda_t$ may be deterministic or random, not the process.
– theQman
Jul 29 at 18:17





Sorry, I mean that the parameter $lambda_t$ may be deterministic or random, not the process.
– theQman
Jul 29 at 18:17
















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