# Fractional Poisson Analysis in Dimension one

@inproceedings{Bendong2022FractionalPA, title={Fractional Poisson Analysis in Dimension one}, author={Jerome B. Bendong and Sheila Menchavez and Jos{\'e} Lu{\'i}s da Silva}, year={2022} }

In this paper, we use a biorthogonal approach (Appell system) to construct and characterize the spaces of test and generalized functions associated to the fractional Poisson measure π λ,β , that is, a probability measure in the set of natural (or real) numbers. The Hilbert space L 2 ( π λ,β ) of complex-valued functions plays a central role in the construction, namely, the test function spaces ( N ) κπ λ,β , κ ∈ [0 , 1] is densely embedded in L 2 ( π λ,β ) . Moreover, L 2 ( π λ,β ) is also…

## One Citation

### Biorthogonal Approach to Infinite Dimensional Fractional Poisson Measure

- Mathematics
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In this paper we use a biorthogonal approach to the analysis of the inﬁnite dimensional fractional Poisson measure π βσ , 0 < β ≤ 1 , on the linear space D (cid:48) . The Hilbert space L 2 ( π βσ )…

## References

SHOWING 1-10 OF 27 REFERENCES

### Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach

- Mathematics
- 1996

Framework.- Applications to Stochastic Ordinary Differential Equations.- Stochastic Partial Differential Equations Driven by Brownian White Noise.- Stochastic Partial Differential Equations Driven by…

### Principles and Techniques in Combinatorics

- Mathematics
- 1992

Permutations and combinations binomial coefficients and multinomial coefficients the Pigeonhole principle and Ramsey numbers the principle of inclusion and exclusion generating functions recurrence…

### Fractional Poisson Law

- Mathematics
- 2000

We consider a Poisson process with random intensity for which the distribution of intervals between jumps is described by an equation with fractional derivatives. The distribution of random intensity…

### NIST Handbook of Mathematical Functions

- Mathematics
- 2010

This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators and is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun.

### Sur une classe de polynômes

- Mathematics
- 1880

© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1880, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.…

### On the Fractional Poisson Process and the Discretized Stable Subordinator

- MathematicsAxioms
- 2015

The Laplace-Laplace formalism is applied to the fractional Poisson process whose waiting times are of Mittag-Leffler type and to a renewal process whose waits are of Wright type, and yields as diffusion limits the inverse stable and the stable subordinator, respectively.

### 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…