Îto Calculus?

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I'm a bit curious as well about how /sci/ bros into calculus.

My masters thesis topic pivoted from being about plant ecology (lame/boring) to focusing on physics modelling (interesting/based) which I'm keeping my head above water on, even though I've never taken a physics class and I barely squeaked through Calc 2 (~7 years ago when I was a dumb nihilistic kid - I'd do much better now that I actually care about learning).

I could really use some kind of thoroughly distilled undergrad-level primer book to drill the basics of this stuff into my head.

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>>8278414
Mathematica has some nice tools for SDEs. Here's what the equations on the "Heston model" Wikipedia page look like with parameters that I pulled out of my ass.

>>8278414
I used to do a lot of studying of that stuff back when I went through a mathematical finance phase. Unfortunately I've lost all of my notes from that.

Ultimately though they're basically just integrals of random processes. It's seeing what you'd get assuming the process follows a certain distribution. A CDF is essentially the distribution of the Ito integral of the random process that is distributed according to the corresponding PDF.

>>8278470
>Wiener process
Top kek

>>8278785
That's exactly what a random walk is called.

Get your head out of the gutter.

>>8278414
Oksendal

>>8278778
this is wrong

>>8279054
It was intended as a simplification, but please explain how it's wrong.

>>8279115
a CDF is a function but the Ito integral of a random process is a random variable

>>8279124
Yes, which is why I said the CDF is the distribution OF that integral.

>>8278778
>I went through a mathematical finance phase

OP here and I'm going through this phase now. What phase comes after this one?

>>8279232
I think after that I went into a circuit design phase, which has lasted into the present, seeing as I'm still an EE major.

>>8279130
Sorry, I misread it. But it's still wrong or at least misleading- a CDF and the corresponding PDF both correspond to the same distribution

>>8279239
Right, but the PDF of the distribution of the integral is essentially the CDF of the distribution of the integrand.

>>8279238
Ah, I'm an Applied Math major so I hope this phase will last for me.