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A Representation of Independent Increment Processes without Gaussian Components
A Representation of Independent Increment Processes without Gaussian Components,10.1214/aoms/1177692395,The Annals of Mathematical Statistics,Thomas S
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A Representation of Independent Increment Processes without Gaussian Components
(
Citations: 70
)
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Thomas S. Ferguson
,
Michael J. Klass
Journal:
The Annals of Mathematical Statistics
, vol. 43, no. 1972, pp. 16341643, 1972
DOI:
10.1214/aoms/1177692395
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projecteuclid.org
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Citation Context
(23)
...
Ferguson and Klass (1972)
describe how a L´ evy process can be expressed as a transformation of a Poisson process...
...The stochastic integral can be expressed using the
Ferguson and Klass (1972)
method as...
J. E. Griffin
.
The Ornstein–Uhlenbeck Dirichlet process and other timevarying proces...
...
Ferguson and Klass (1972)
, Damien, Laud and Smith (1995), Walker and Damien (1998, 2000) and Wolpert and Ickstadt (1998)...
Antonio Lijoi
,
et al.
Models beyond the Dirichlet process
...The infinitely divisible law that we obtain as the limit of (Sn)n≥1 must have a L´evy measure � which satisfies the condition R 1 0 x�(dx) < ∞. This is a limitation which has to do with the method that we use, based on the Ferguson
K
lass [15] representation of an infinitely divisible law...
...Relation (16) allows us to invoke a powerful (and highly nontrivial) construction, due to Ferguson and Klass (see [
15
])...
...Remark 3.10 Lemma 3.3 can be extended to a Poisson process whose intensity � is an arbitrary L´evy measure on (0, ∞). More precisely, using the Theorem
o
f [15], one can prove that if N ∗ = P i≥1 �Ui is a Poisson process on (0, ∞), whose intensity � is a L´evy measure, then the random variable Y := P i≥1 (Ui −ci) is finite a.s...
Raluca M. Balan
,
et al.
Convergence of Point Processes with Weakly Dependent Points
...This result is proved by Khintchine [4] first, and later rediscovered by Ferguson and Klass [
3
]...
Zishan Su
,
et al.
Asymptotic distributions of standardized Ψsums for a class of distrib...
...characteristic function of Z is equal to: (
12
) ψ(u) =...
F. COMTE
,
et al.
NONPARAMETRIC ADAPTIVE ESTIMATION FOR PURE JUMP L
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Citations
(70)
The Ornstein–Uhlenbeck Dirichlet process and other timevarying processes for Bayesian nonparametric inference
(
Citations: 3
)
J. E. Griffin
Journal:
Journal of Statistical Planning and Inference  J STATIST PLAN INFER
, vol. 141, no. 11, pp. 36483664, 2011
Nonparametric adaptive estimation for pure jump Lévy processes
(
Citations: 5
)
Fabienne Comte
,
Valentine GenonCatalot
Journal:
Annales De L Institut Henri Poincareprobabilites Et Statistiques  ANN INST HENRI POINCAREPROB
, vol. 46, no. 2010, pp. 595617, 2010
On a Class of Random Probability Measures with General Predictive Structure
(
Citations: 2
)
STEFANO FAVARO
,
IGOR PRÜNSTER
,
STEPHEN G. WALKER
Journal:
Scandinavian Journal of Statistics  SCAND J STATIST
, pp. nono, 2010
Incremental moments and H\"older exponents of multifractional multistable processes
(
Citations: 1
)
Ronan Le Guével
,
Jacques LévyVéhel
Published in 2010.
Bayesian density estimation and model selection using nonparametric hierarchical mixtures
(
Citations: 1
)
Raffaele Argiento
,
Alessandra Guglielmi
,
Antonio Pievatolo
Journal:
Computational Statistics & Data Analysis  CS&DA
, vol. 54, no. 4, pp. 816832, 2010