# Talk:Lévy process

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## Spelling

Corrected spelling of Khintchine. See here http://www.maths.bath.ac.uk/~ak257/LCSB/part1.pdf also Philip Protter's "Stochastic Integration and Differential Equations" —Preceding unsigned comment added by 155.198.190.241 (talk) 18:25, 18 November 2008 (UTC)

## Lévy-Khintchine representation

I didn't get this part. There are many terms that are used without previous definition, and the conclusion so one can see that a purely continuous Lévy process is a Brownian motion with drift is in apparent contradiction with the article Infinite divisibility (probability), where it's implied that we could generate a Lévy process using the Cauchy distribution, that would not generate a tame Brownian motion but a wild Lévy flight. Albmont 17:54, 29 October 2007 (UTC)

Ok, now I get it. See these lectures by Álvaro Cartea. In short, all other Lévy processes are (everywhere) discontinuous. The Cauchy process would be discontinuous everywhere too. Albmont (talk) 20:30, 19 November 2007 (UTC)

## Proper Definition and Levy-Ito Decomposition

I think it would be nice to have a proper mathematical definition of a Levy process instead of a paragraph of woffle. Also I think that the Levy-Ito decomposition should be included as it is one of the fundamental properties of a Levy process. I am willing to write these up unless anyone objects... Hyperbola 15:44, 22 February 2009 (UTC)

## Lévy measure

Article Lévy measure redirects here, but there is no mention/definition. Melcombe (talk) 09:56, 11 May 2010 (UTC).

I added a definition of the Lévy measure (Sept 2012)

## References needed

I think this article desperately needs some good references. The article by Applebaum is not sufficient. In particular it makes no mention at all of the asserted polynomial nature of the moments. Pere Callahan (talk) 00:20, 21 June 2010 (UTC) I have added three more references: graduate textbooks which include introductory sections on Levy processes with detailed proofs of the result given here. (Sept 2012) — Preceding unsigned comment added by 90.61.162.95 (talk) 20:41, 3 September 2012 (UTC)

## Cádlág modification

There should be some clarification of what exactly càdlàg modification is! Following the càdlàg link does not make it clearer. --62.107.83.243 (talk) 21:39, 17 November 2010 (UTC)

## Statistics

The article focuses on probability mathematics. It would be useful to include more on probability models of real phenomena and statistics. For the latter, see Michael Sorensen and co-author on Exponential Familes of Stochastic Processes, etc.: Steffan Iacus (sic) had a Springer monograph on inference for SDEs driven by exponential families, also.  Kiefer.Wolfowitz  (Discussion) 13:18, 13 April 2011 (UTC)

## Constructing a stochastic probability measure

Is this whole section even necessary? It seems excessive and indulgent and not particularly specific to the article at hand. 128.122.20.85 (talk) 00:56, 30 June 2011 (UTC)

I agree: this section is not necessary. It has nothing to do with Levy processes. — Preceding unsigned comment added by 86.195.224.109 (talk) 21:40, 27 August 2012 (UTC)