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Anonymous
How to compute stochastic integrals ? 2017-01-13 03:58:06 Post No. 8598661
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How to compute stochastic integrals ? 2017-01-13 03:58:06 Post No. 8598661
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Hello /sci/, mathsphi anon here. I'm working on brownian motion, and stochastic integrals. I saw that [math] \int_0^t . dW_s [/math] is a L2 limit and other things like that. But I have difficulties with calculus. For instance, I can compute :
[math] \int_0^t f(s) dW_s = f(t)W_t - \int_0^t f(s)W_sds[/math] or the well-knowed :
[math] \int_0^t W_sdW_s = \frac12 ( W_t^2 - t)[/math]
But what if I want to compute :
[math]\int_0^t W_s^2 dW_s[/math] or [math]\int_0^t \exp(W_s) dW_s[/math] ?
Is there a way to compute it ? Must I write something like
[eqn] \sum_{i=0}^n \varphi(W_{ \frac{it}{n} })( W_{\frac{(i+1)t}{t}} - W_{ \frac{it}{n} })[/eqn] everytime I want to make an exercice ?
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i have no idea what you are talking about but that looks like italy if you turn it sideways
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>>8598776
Thanks for bump.
It's my Python simulation.
Pic related is more like Germany ?
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>>8598661
matplotlib is cool
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>>8598661
Interesting topic OP. Look up Ito's Lemma.
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>>8598661
Hey OP, I was considering majoring in either math or philosophy, and I can't do both. What do you think I should do?
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>>8599377
Maths.
You will make some shekels, and it would be very difficult to live as a "philosopher", only the best have this privilege.
While you can have very decent job even if you are not a top mathematicians.
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>>8599406
thx fampai.
But to be exact, which one did you find more interesting? If I go to PhD I might consider philosophy.
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>>8599411
Well, I do not know about philosophy. But the thing is that you can learn philosophy by yourself, you need time and books. But learning maths alone is... oustandingly hard.
Btw if you consider PhD in maths you can be swallowed immediately by firms like IBM or Boeing for 100 000 $ a year. You can earn some money and maybe, if you are fed up with your job, make your own business.
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>>8599466
Thanks for the good advice my dude. I look forward to that >300k starting.
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>>8598661
The 2 numerical methods I know:
Euler-Maruyama and Milstein (I & II). I think there's some runge-kutta shit but never used it.
Don't know about FEM, I know there are some papers on it but honestly the study of convergence of FEM for these distributions must be a PITA. I don't even know if they exist in [math]H^m(\Omega)[/math]. Probably not.
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