RECORD
Structure of infinitely divisible semimartingales
Probability · Submitted 7 Sep 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This paper gives a complete characterization of infinitely divisible semimartingales, i.e., semimartingales whose finite dimensional distributions are infinitely divisible.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
This paper gives a complete characterization of infinitely divisible semimartingales, i.e., semimartingales whose finite dimensional distributions are infinitely divisible. An explicit and essentially unique decomposition of such semimartingales is obtained. A new approach, combining series decompositions of infinitely divisible processes with detailed analysis of their jumps, is presented. As an ilustration of the main result, the semimartingale property is explicitely determined for a large class of stationary increment processes and several examples of processes of interest are considered. These results extend Stricker's theorem characterizing Gaussian semimartingales and Knight's theorem describing Gaussian moving average semimartingales, in particular.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This paper gives a complete characterization of infinitely divisible semimartingales, i.e., semimartingales whose finite dimensional distributions are infinitely divisible. | contribution 0.82 | 0.93 | 0.76 | asserted 1.00 |
| s1 | An explicit and essentially unique decomposition of such semimartingales is obtained. | result 0.91 | 0.95 | 0.38 | asserted 1.00 |
| s2 | A new approach, combining series decompositions of infinitely divisible processes with detailed analysis of their jumps, is presented. | method 0.94 | 0.94 | 0.07 | asserted 1.00 |
| s3 | As an ilustration of the main result, the semimartingale property is explicitely determined for a large class of stationary increment processes and several examples of processes of interest are considered. | result 0.59 | 0.92 | 0.09 | asserted 1.00 |
| s4 | These results extend Stricker's theorem characterizing Gaussian semimartingales and Knight's theorem describing Gaussian moving average semimartingales, in particular. | interpretation 0.82 | 0.71 | 0.10 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v3
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
This paper gives a complete characterization of infinitely divisible semimartingales, i.e., semimartingales whose finite dimensional distributions are infinitely divisible. An explicit and essentially unique decomposition of such semimartingales is obtained. A new approach, combining series decompositions of infinitely divisible processes with detailed analysis of their jumps, is presented. As an ilustration of the main result, the semimartingale property is explicitely determined for a large class of stationary increment processes and several examples of processes of interest are considered. These results extend Stricker's theorem characterizing Gaussian semimartingales and Knight's theorem describing Gaussian moving average semimartingales, in particular.
Human review
How the literature uses it
2 arXiv papers cite this in 6 sentences
Papers citing it · 5 sentences without a confident label
Uses its method or tool 1 paper
-
However, in this subsection we closely follow the recent results of [ref] .
Ambit fields: survey and new challenges · Semimartingale property with respect to $(ℱ^L_t)$ · 0.83
What it cites · 2 sentences without a confident label
Cites as support 1 paper
-
The process $$ is of finite variation by [ref] because $g(·,v)$ is absolutely continuous on $$ and $ġ(·, v)= ḟ(·, v)$ satisfies [ref]–[ref].
Characterization of the finite variation property for a class of stationary increment infinitely divisible processes · Some stationary increment semimartingales · 0.98
Cites as background 1 paper
-
Below we will recall the conditions from [ref] under which [ref] or [ref] hold.
Characterization of the finite variation property for a class of stationary increment infinitely divisible processes · Some stationary increment semimartingales · 0.83
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.