1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Stochastic Processes

  1. Feb 16, 2008 #1
    1. The problem statement, all variables and given/known data
    I need someone to reassure me (or correct me) on this problem:

    The process [tex] X(t) = e^{At} [/tex] is a family of exponentials depending on the random variable A.
    Express the mean [tex] \eta(t) [/tex], the autocorrelation [tex] R(t_1,t_2) [/tex], and the first order density f(x,t) of X(t) in terms of the density [tex] f_a(a) of A [/tex]

    2. Relevant equations

    [tex] f(x,t) = \frac {\partial F(x,t)} {\partial x} [/tex]
    [tex] \eta (t) = \int_{-\infty}^{\infty} xf(x,t)dx [/tex]
    [tex] R(t_1,t_2) = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} x_1 x_2 [/tex]
    [tex]f(x_1,x_2;t_1,t_2)dx_1 dx_2 [/tex]

    3. The attempt at a solution

    [tex] f_a(a) = ae^a [/tex]
    [tex] f(x,t) = ae^{at} [/tex]
    [tex] \eta(t) = \int_{-\infty}^{\infty} a^2 e^{at} da [/tex]
    [tex] R(t_1,t_2) = \int_{-\infty}^{\infty} a^4 e^{at_1} e^{at_2} da
    Last edited: Feb 16, 2008
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted