## 35 Citations

### Time-changed space-time fractional Poisson process

- MathematicsStochastic Analysis and Applications
- 2021

Abstract In this paper, we introduce and study a time-changed version of the space-time fractional Poisson process (STFPP) by time changing it by an independent Lévy subordinator with finite moments…

### Time-changed Poisson processes of order k

- MathematicsStochastic Analysis and Applications
- 2019

Abstract In this article, we study the Poisson process of order (PPoK) time-changed with an independent Lévy subordinator and its inverse, which we call, respectively, as TCPPoK-I and TCPPoK-II,…

### Some Time-changed fractional Poisson processes

- Mathematics
- 2017

In this paper, we study the fractional Poisson process (FPP) time-changed by an independent Levy subordinator and the inverse of the Levy subordinator, which we call TCFPP-I and TCFPP-II,…

### Fractional Poisson Process Time-Changed by Lévy Subordinator and Its Inverse

- Mathematics
- 2017

In this paper, we study the fractional Poisson process (FPP) time-changed by an independent Lévy subordinator and the inverse of the Lévy subordinator, which we call TCFPP-I and TCFPP-II,…

### Fractional Poisson Process Time-Changed by Lévy Subordinator and Its Inverse

- MathematicsJournal of Theoretical Probability
- 2017

In this paper, we study the fractional Poisson process (FPP) time-changed by an independent Lévy subordinator and the inverse of the Lévy subordinator, which we call TCFPP-I and TCFPP-II,…

### Time-inhomogeneous fractional Poisson processes defined by the multistable subordinator

- MathematicsStochastic Analysis and Applications
- 2018

Abstract The space-fractional and the time-fractional Poisson processes are two well-known models of fractional evolution. They can be constructed as standard Poisson processes with the time variable…

### On fractional tempered stable processes and their governing differential equations

- MathematicsJ. Comput. Phys.
- 2015

### Randomly Stopped Nonlinear Fractional Birth Processes

- Mathematics
- 2011

We present and analyze the nonlinear classical pure birth process 𝒩(t), t > 0, and the fractional pure birth process 𝒩ν(t), t > 0, subordinated to various random times. We derive the state…

### A fractional counting process and its connection with the Poisson process

- Mathematics
- 2015

We consider a fractional counting process with jumps of amplitude $1,2,\ldots,k$, with $k\in \mathbb{N}$, whose probabilities satisfy a suitable system of fractional difference-differential…

### Counting processes with Bernštein intertimes and random jumps

- MathematicsJournal of Applied Probability
- 2015

In this paper we consider point processes Nf (t), t > 0, with independent increments and integer-valued jumps whose distribution is expressed in terms of Bernštein functions f with Lévy measure v. We…

## References

SHOWING 1-10 OF 26 REFERENCES

### The Fractional Poisson Process and the Inverse Stable Subordinator

- Mathematics
- 2010

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.…

### On doubly stochastic Poisson processes

- MathematicsMathematical 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

- Mathematics
- 2009

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

- Mathematics
- 2011

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

- Mathematics
- 2009

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

- MathematicsJournal of Applied Probability
- 2004

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

- Mathematics
- 2011

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

- Mathematics
- 2004

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…