Time-changed Poisson processes

@article{Kumar2011TimechangedPP,
  title={Time-changed Poisson processes},
  author={A. Kumar and Erkan Nane and Palaniappan Vellaisamy},
  journal={Statistics \& Probability Letters},
  year={2011},
  volume={81},
  pages={1899-1910}
}
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35 Citations
Highly Influential Citations
3
Background Citations
21
Methods Citations
1
Results Citations
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35 Citations

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References

SHOWING 1-10 OF 26 REFERENCES

The Fractional Poisson Process and the Inverse Stable Subordinator

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process.…

Triangular array limits for continuous time random walks

Fractional Poisson process

On doubly stochastic Poisson processes

  • J. Kingman
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1964
The class of stationary point processes known as ‘doubly stochastic Poisson processes’ was introduced by Cox (2) and has been studied in detail by Bartlett (1). It is not clear just how large this…

Fractional Poisson processes and related planar random motions

We present three different fractional versions of the Poisson process and some related results concerning the distribution of order statistics and the compound Poisson process. The main version is…

First-exit times of an inverse Gaussian process

Abstract The first-exit time process of an inverse Gaussian Lévy process is considered. The one-dimensional distribution functions of the process are obtained. They are not infinitely divisible and…

Brownian subordinators and fractional Cauchy problems

A Brownian time process is a Markov process subordinated to the absolute value of an independent one-dimensional Brownian motion. Its transition densities solve an initial value problem involving the…

Limit theorems for continuous-time random walks with infinite mean waiting times

A continuous-time random walk is a simple random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has…

Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion

In this paper Fokker-Planck-Kolmogorov type equations associated with stochastic differential equations driven by a time-changed fractional Brownian motion are derived. Two equivalent forms are…

Lévy Processes and Stochastic Calculus

Levy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random…