@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.

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

@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.

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.

- February 24th, 2020, 5:49 am
- Forum: Politics Forum
- Topic: FSU, Toby Young, Eugenics & Wilmott.com
- Replies:
**48** - Views:
**1119**

Frank Bruni -- Liberal Censorship -- Bill Maher show

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

Jordan Peterson -- Bill Maher show

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

Jordan Peterson -- Bill Maher show

- February 21st, 2020, 8:28 pm
- Forum: Politics Forum
- Topic: FSU, Toby Young, Eugenics & Wilmott.com
- Replies:
**48** - Views:
**1119**

Speaking of free speech and porn:

Why Every Member of Congress Gets a Monthly Porn Delivery

Why Every Member of Congress Gets a Monthly Porn Delivery

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

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/...

- February 16th, 2020, 12:15 am
- Forum: Politics Forum
- Topic: Trump -- the last 100 days
- Replies:
**3298** - Views:
**139578**

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

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

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...

- February 15th, 2020, 7:22 pm
- Forum: Politics Forum
- Topic: Trump -- the last 100 days
- Replies:
**3298** - Views:
**139578**

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...

- 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**

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"

- February 13th, 2020, 2:34 pm
- Forum: Numerical Methods Forum
- Topic: About solving a transport equation
- Replies:
**157** - Views:
**53214**

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...

- February 13th, 2020, 5:52 am
- Forum: Student Forum
- Topic: Silly questions
- Replies:
**94** - Views:
**14996**

I demand a recount! Anyway, it's not even 6am -- don't you people sleep?

- February 13th, 2020, 5:34 am
- Forum: Student Forum
- Topic: Silly questions
- Replies:
**94** - Views:
**14996**

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...

- February 13th, 2020, 1:30 am
- Forum: Student Forum
- Topic: Silly questions
- Replies:
**94** - Views:
**14996**

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...

- February 13th, 2020, 1:23 am
- Forum: Student Forum
- Topic: Silly questions
- Replies:
**94** - Views:
**14996**

That works.Via gamma fn, looks messy!

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 [$]\Gamma(n+1)[$].

- February 10th, 2020, 6:30 am
- Forum: Numerical Methods Forum
- Topic: About solving a transport equation
- Replies:
**157** - Views:
**53214**

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...

- February 7th, 2020, 3:45 pm
- Forum: Numerical Methods Forum
- Topic: About solving a transport equation
- Replies:
**157** - Views:
**53214**

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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