# Search results

1. ### Stochastic ODE

Hello all, I have run into this problem, and being that I know nothing about stochastic DiffyQ I am trying to toy around with it. Basically, the following is a boiled down version of my problem: I have a probability density function that is given: p(t) and let's say we pick 1 value from...
2. ### Decomposing an operator

In case this wasn't clear, I'll write it over this way: (L-G)v = y Lv1=y Gv2=0 or equivalently: (L-G)-1y=v L-1y=v1 G-10=v2 v1 and v2 and v are not equal, they are different. I'd like to have an equation for v in terms of v1 and v2.
3. ### Decomposing an operator

So I am trying to decompose a linear operator A, in the following manner. I am trying to solve Ax=y for x, and I also have that A=(L-G), so I am trying to solve (L-G)x=y. y is given, and so are L, A, and G. Now, I also know the solutions to Lx1=y and Gx2=0. I'd like to somehow find an...
4. ### Electromagnetic brain?

LFP (local field potentials) can be anywhere from <1 to 40 Hz. There is currently a lot of research going into what exactly these fields are (that is, are they action potential spiking, or are they subthreshold membrane fluctuations, or are they representative of synaptic input at the...
5. ### Trying to understand why integration is inverse of differentiation

Think of this integral, with respect to your image: I(a)=\int_0^a f(x) dx a is your endpoint, and obviously the integral changes as you change a. Now, we want to understand why the derivative of I gives back f(x). Basically, think of a changing from some value b to b+epsilon. The amount that a...
6. ### Finding the inverse of an integral transform

Oh Im dumb:T[f(x)](k)=\int_{-\infty}^\infty e^{- 2 \pi i k x}e^{ 2 \pi i k a}f(x)dx=e^{ 2 \pi i k a} \int_{-\infty}^\infty e^{- 2 \pi i k x}f(x)dx=e^{ 2 \pi i k a}\mathcal{F}[f(x)] So uhh, actually I'm still not sure what that makes the inverse of T
7. ### Finding the inverse of an integral transform

Hi, I've defined an integral transform that I'll call T (obviously very similar to the fourier transform): T[f(x)](k)=\int_{-\infty}^\infty e^{- 2 \pi i k (x-a)}f(x)dx=\int_{-\infty}^\infty e^{- 2 \pi i k x}e^{ 2 \pi i k a}f(x)dx where a is a given parameter. perhaps we can call this the "a...
8. ### Multivariate Distributions, Moments, and Correlations

i actually start with only the joint distribution, f(x,y). Then I am trying to find a relationship relating the moments of the conditional probability f(x|y) to the moments of the conditional probability f(y|x). I'm running into a slight issue taking the inverse Fourier transform of e^k...
9. ### Multivariate Distributions, Moments, and Correlations

yea thanks, so I've been messing around a bit, and I think I've almost got it figured out (just need to make everything pretty for my specific example). But in general, this is what I have: Given the moments of either conditional distribution functions, you can recreate the characteristic...
10. ### Multivariate Distributions, Moments, and Correlations

So if I start with a multivariate distribution f(x,y), I can find the marginal distributions, the conditional probability distributions, all conditional moments, and by the law of iterated expectations, the moments of both X and Y. It seems to me that I should be able to relate the conditional...
11. ### Moment generating functions

Thanks for your help, I don't know how I didn't get this on my own, ugh. Just in case someone uses this thread in the future: You still do the series expansion around 0 (not m) to get moments about a point m.
12. ### Moment generating functions

Hello, I was wondering if anyone knew how to find a moment generating function about the mean. What I want is a function whose power series expansion gives you a power series where the x^n coefficient is the nth moment about the mean. normally, moment generating functions give you the raw...
13. ### Wavefunction Dimensionality

Hey Guys, I'm getting a bit confused on the dimensionality of the wavefunction. I've seen the wavefunction described as: (1) A vector of norm 1 in a finite dimensional Hilbert Space (2) A vector of norm 1 in an infinite dimensional Hilbert Space (3) A continuos function (it is my...