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Q: Tag synonyms: Inconsistencies

Paul FrostMany tags have synonyms. My understanding is that there are "primary" tags with one or more synonyms. If somebody uses a synonym, then the this tag is automatically replaced by the primary tag. "Synonym" tags should not occur in the tag list at the bottom of a question, but they are searchable. F...

Here is a related SEDE query: Tag synonyms where both tags have some questions - on the main site and on meta. I see there only three instances not listed in the current revisions of the question, namely congruences, expectation and stability-in-odes. — Martin Sleziak Mar 28 at 9:19
I suspect that those examples you list are tags where a synonym was created and the two tags haven't been merged. This has some consequences for searching in those tags: Tag synonyms and searching. — Martin Sleziak Mar 28 at 9:24
@MartinSleziak You are certainly right that a synonym was created and the two tags have not been merged. But in most cases they were merged and in my question I suggested to catch up with merging. — Paul Frost Mar 28 at 9:59
 
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Q: If $a,b,c \in R$ such that $a < b < c < d$ , show that $(x-a)(x-c) + 2(x-b)(x-d) = 0$ has real and distinct roots .

Ash_Blanc If $a,b,c \in R$ such that $a < b < c < d$ , show that $(x-a)(x-c) + 2(x-b)(x-d) = 0$ has real and distinct roots . I'm not getting good manipulation idea to show discriminant positive , also wherever I searched i found only same not much intuitive solution . I m seeking for good intuitive sol...

Jun 13 at 14:23, by Martin Sleziak
Questions where the tag was added/removed (including the editors): https://data.stackexchange.com/math/query/1105163/questions-which-had-the-given-tag-including-the-editor-who-added-it?tagname=theory-of-equations https://data.stackexchange.com/math/query/1038474/questions-which-no-longer-have-the-given-tag-including-the-editor?tagName=theory-of-equations
The tag (theory-of-equations) was previously discussed on meta and the consensus was that the tag should be removed. I'd say that if you still think that such tag should exist, you should probably start a discussion on meta about that tag - to see whether other users of the site consider such tag to be useful. — Martin Sleziak 1 min ago
11:54 AM
@MartinSleziak i didn't know about it sorry but I m fine with removal of this tag — Ash_Blanc 15 mins ago
 
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Q: "Heuristic" vs. Rigorous Ito's Lemma

Jan StullerAssuming $X_t$ is a standard Brownian motion and $t$ is the time variable, I have learned to derive Ito's lemma for a function $F(X_t, t)$ using the following results: For any finite $\delta t > 0$ and a standard Brownian motion $X_t$, we can argue that: \begin{align*} \tag{1} \delta X_t := X(\de...

In mathematics, Itô's lemma or Itô's formula (also called the Itô–Doeblin formula, especially in the French literature) is an identity used in Itô calculus to find the differential of a time-dependent function of a stochastic process. It serves as the stochastic calculus counterpart of the chain rule. It can be heuristically derived by forming the Taylor series expansion of the function up to its second derivatives and retaining terms up to first order in the time increment and second order in the Wiener process increment. The lemma is widely employed in mathematical finance, and its best known...
Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and stochastic differential equations. The central concept is the Itô stochastic integral, a stochastic generalization of the Riemann–Stieltjes integral in analysis. The integrands and the integrators are now stochastic processes: where H is a locally square-integrable process adapted to the filtration generated by X (Revuz & Yor 1999, Chapter IV), which is a Brownian motion or, more generally, a se...

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