Talk:Lévy process

message: 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)
thread_title:  Spelling 

message: 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)
replies: text: 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)
thread_title:  Lévy-Khintchine representation 

message: 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)
thread_title:  Proper Definition and Levy-Ito Decomposition 

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

message: 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)
thread_title:  References needed 

message: 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)
thread_title: Cádlág modification 

message: 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)
thread_title:  Statistics 

message: 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)
thread_title: Constructing a stochastic probability measure

message: Substituted at 20:05, 1 May 2016 (UTC)
thread_title: Assessment comment

message: In the article is says:
If  X = (X_t)_{t\geq 0}  is a Lévy process, then its characteristic function  \phi_X(\theta)  is given by
:\phi_X(\theta) := \mathbb{E}\Big[e^{i\theta X} \Big] = \exp \Bigg( ai\theta - \frac{1}{2}\sigma^2\theta^2 + 
\int_{\mathbb{R}\backslash\{0\}} \big( e^{i\theta x}-1 -i\theta x \mathbf{I}_{|x|<1}\big)\,\Pi(dx) \Bigg)
What do you mean here by  \mathbb{E}\Big[e^{i\theta X} \Big]? I guess it should be  \mathbb{E}\Big[e^{i\theta X_1} \Big]. The distribution of a Lévy process X is uniquely given by the distribution of X_1. I guess you are looking at the characteristic function of X_1 here. 68.174.156.215 (talk) 03:33, 20 July 2016 (UTC)
thread_title: Characteristic function of a process