Talk:Semimartingale

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Don't you need certain conditions in a super or sub martingale in order to be semimartingale? I mean, does not Doob theorem require certain assumptions?

Every cadlag sub or supermartingale is a semimartingale.Roboquant (talk) 14:25, 3 March 2008 (UTC)[reply]

A related question: I assume any martingale is a local martingale, and that the function "zero" is a càdlàg adapted process of locally bounded variation. If so, it seems by the first definition that any martingale should also be a semimartingale, but the examples only list càdlàg martingales. Why is that? LachlanA (talk) 22:05, 2 June 2008 (UTC)[reply]

Local martingales are usually (always?) defined to be cadlag, whereas there's no such restriction on general martingales. So every cadlag martingale is a semimartingale, but a martingale doesn't have to be a semimartingale. Roboquant (talk) 22:36, 3 June 2008 (UTC)[reply]

Integral H.X

The text refers to "the integral H.X". Could someone please add a hyperlink to the correct "type" of integral, for those of us who think integral=Riemann... Thanks LachlanA (talk) 22:13, 2 June 2008 (UTC)[reply]

You mean in the "Alternative definition" section? It is defined on the following line. I guess you could call it an Ito integral, but I don't think that is really right, as it's just a very special case for simple step functions which is defined explicitly.Roboquant (talk) 22:48, 3 June 2008 (UTC)[reply]

Dr. Podolskij's comment on this article

Dr. Podolskij has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"Itō processes, which satisfy a stochastic differential equation of the form dX = σdW + μdt are semimartingales. Here, W is a Brownian motion and σ, μ are adapted processes." When stating the stochastic differential equation it is better to write (in latex) "dX_t=\sigma_t dW_t + \mu_t dt", so adding the time variable t.

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Podolskij has published scholarly research which seems to be relevant to this Wikipedia article:

Reference : Mark Podolskij & Daniel Ziggel, 2008. "New tests for jumps: a threshold-based approach," CREATES Research Papers 2008-34, School of Economics and Management, University of Aarhus.

ExpertIdeasBot (talk) 18:31, 27 June 2016 (UTC)[reply]

Two definitions that are not equal?

Just a question from an outsider: There is a definition, an alternative definition, and then this sentence: "The Bichteler-Dellacherie Theorem states that these two definitions are equivalent"

The logic contradiction is obvious: How can have something two valid definitions that are "not equivalent"? Could one of those definitions be wrong? Why is this not specified? Or maybe I'm getting it all wrong here? --94.222.27.254 (talk) 11:16, 29 November 2016 (UTC)[reply]

Correct, you can never have two definitions of the same thing that are not equivalent, unless you've made a mistake.

But it is standard mathematical procedure to define something two ways, then prove the definitions are equivalent. Then you are forced to do the proof (or refer to it). If the definitions are inequivalent, you've written a contradiction; if you don't do or cite the proof, your presentation is incomplete. 2A02:1210:2642:4A00:7819:2810:4F3E:34BC (talk) 20:05, 12 October 2023 (UTC)[reply]

Section needs more detail

The section Continuous-time and discrete-time components of a semimartingale needs more complete definitions and discussions to be readable. The components $X^{\mathrm {qc} }$ and $X^{\mathrm {dp} }$ are not really defined, just kind of alluded to "in passing" -- too quickly. 2A02:1210:2642:4A00:7819:2810:4F3E:34BC (talk) 19:56, 12 October 2023 (UTC)[reply]