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by Alan
February 24th, 2020, 3:56 pm
Forum: General Forum
Topic: Proof for square-root-of-time rule
Replies: 3
Views: 299

Re: Proof for square-root-of-time rule

@mathdude,
 bearish's iid argument is rigorous as long as you interpret "returns" as [$]x_t = \log S_t/S_{t-1}[$], and the variance of [$]x_t[$] exists.
by Alan
February 24th, 2020, 5:49 am
Forum: Politics Forum
Topic: FSU, Toby Young, Eugenics & Wilmott.com
Replies: 48
Views: 1119

Re: FSU, Toby Young, Eugenics & Wilmott.com

Frank Bruni -- Liberal Censorship -- Bill Maher show

plus, another good clip from his show, on the same topic

Jordan Peterson -- Bill Maher show
by Alan
February 21st, 2020, 8:28 pm
Forum: Politics Forum
Topic: FSU, Toby Young, Eugenics & Wilmott.com
Replies: 48
Views: 1119

Re: FSU, Toby Young, Eugenics & Wilmott.com

by Alan
February 16th, 2020, 4:52 am
Forum: Politics Forum
Topic: Trump -- the last 100 days
Replies: 3298
Views: 139578

Re: Trump -- the last 100 days

Thanks, Alan.  Mulling it over. :D What comes immediately to mind is ppauper, actually, and the photo he liked to post whenever writing about AOC, e.g.,: ppauper:  the "democratic socialists" are fighting amongst themselves. Sandy Ocasio wants to tax the rich at 70% https://cdn.cnn.com/cnnnext/dam/...
by Alan
February 16th, 2020, 12:15 am
Forum: Politics Forum
Topic: Trump -- the last 100 days
Replies: 3298
Views: 139578

Re: Trump -- the last 100 days

There's no accounting for taste. I'd like to hear trackstar's vote: AOC or:

Image
by Alan
February 15th, 2020, 8:24 pm
Forum: Politics Forum
Topic: Trump -- the last 100 days
Replies: 3298
Views: 139578

Re: Trump -- the last 100 days

My campaign is promoting her to honorary super-model. If elected, we'll throw in a Medal of Freedom: The Presidential Medal of Freedom is awarded by the president of the United States "for especially meritorious contribution to (1) the security or national interests of the United States, or (2) worl...
by Alan
February 15th, 2020, 7:22 pm
Forum: Politics Forum
Topic: Trump -- the last 100 days
Replies: 3298
Views: 139578

Re: Trump -- the last 100 days

Unrelated, but if they're going to subpoena John Bolton, they have to subpoena Hope Hicks. Why? Oh come on :D ... https://i.4pcdn.org/pol/1519870931505.png       I have some news that will make both of you happy.   Hope Hicks expected to return to White House - CNN Feb 13 "Long seen as a stabilizin...
by Alan
February 14th, 2020, 4:14 pm
Forum: Technical Forum
Topic: Is Ito’s lemma applicable to a diffusion process with transition probability?
Replies: 2
Views: 208

Re: Is Ito’s lemma applicable to a diffusion process with transition probability?

Yes, what you are describing is a jump-diffusion. There is an Ito's lemma, a generator, an evolution PIDE, etc, etc. There are many books discussing such processes. Cont and Tankov is good. So is "Option Valuation under Stochastic Volatility II"   :)
by Alan
February 13th, 2020, 2:34 pm
Forum: Numerical Methods Forum
Topic: About solving a transport equation
Replies: 157
Views: 53214

Re: About solving a transport equation

https://en.wikipedia.org/wiki/Burgers%27_equation It would be interesting if Alan and Paul can produce explicit solution for (3A)/(3B) [$]u(x,t) = (ax + b)/(at + 1)[$] for the initial condition [$]u(x,0) = ax + b.[$] I said earlier I don't know much about shocks. But, reading that Wikipedia link, i...
by Alan
February 13th, 2020, 5:52 am
Forum: Student Forum
Topic: Silly questions
Replies: 94
Views: 14996

Re: Silly questions

I demand a recount! Anyway, it's not even 6am -- don't you people sleep?
by Alan
February 13th, 2020, 5:34 am
Forum: Student Forum
Topic: Silly questions
Replies: 94
Views: 14996

Re: Silly questions

The named function just happens to be the answer! Exam question 1: Find the solution of ... Answer: Define [$]\mbox{Lewis}_1[$] as the answer to question 1. Trivially and wlog the answer to question 1 is [$]\mbox{Lewis}_1[$]. Exam question 2: Etc. !!! Well, I'm glad the thread title is called "Sill...
by Alan
February 13th, 2020, 1:30 am
Forum: Student Forum
Topic: Silly questions
Replies: 94
Views: 14996

Re: Silly questions

I think it's just recognizing a "named function". So, take n=6  In Mathematica, what I posted evaluates to [$]1764 - 720 \, \gamma \approx 1348.4[$], using Euler's constant [$]\gamma[$].   Since [$]1348.4 \not= 6[$] that answer's Daniel's question. If it was truly circular, I don't think one could g...
by Alan
February 13th, 2020, 1:23 am
Forum: Student Forum
Topic: Silly questions
Replies: 94
Views: 14996

Re: Silly questions

Via gamma fn, looks messy!
That works. 
Since [$]\frac{d}{dz} \log \Gamma[z] = \psi(z)[$], the Digamma function (A&S, 6.3.1), then 

[$] \frac{dn!}{dn} = \psi(n+1) \, n![$], where of course [$]n![$] is interpreted everywhere as [$]\Gamma(n+1)[$]. 
by Alan
February 10th, 2020, 6:30 am
Forum: Numerical Methods Forum
Topic: About solving a transport equation
Replies: 157
Views: 53214

Re: About solving a transport equation

That's very good and clear, Alan. I get the same solution as your integral approach. BTW do you use some kind of Leibniz' rule for this? I might have missed something along the way. Thanks. No Leibniz rule needed for what I wrote; you solve [$]\frac{dX}{dt} = b(X)[$] simply by writing it as [$]\fra...
by Alan
February 7th, 2020, 3:45 pm
Forum: Numerical Methods Forum
Topic: About solving a transport equation
Replies: 157
Views: 53214

Re: About solving a transport equation

Let me switch to (mostly) book notation for a moment. My main goal in Appendix 1.2 is to make the standard PDE-SDE probability connection for parabolic PDE's on the real line (so no bc). So, for each PDE treated, one finds the (formal) probabilistic solution: run an SDE and take an expectation. Effe...
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