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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)
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)
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:
ExpertIdeasBot ( talk) 18:31, 27 June 2016 (UTC)
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)
The section Continuous-time and discrete-time components of a semimartingale needs more complete definitions and discussions to be readable. The components and 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)
![]() | This article is rated B-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||
|
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)
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)
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:
ExpertIdeasBot ( talk) 18:31, 27 June 2016 (UTC)
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)
The section Continuous-time and discrete-time components of a semimartingale needs more complete definitions and discussions to be readable. The components and 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)