applied stochastic processess
Diffusion equation for probability density distribution of stochastic process Z(t) is
(∂P(z,t))/∂t = -v*(∂P(z,t))/∂z + (B/2)*(∂^2P(z,t))/(∂z^2)
where v and B are constants. Find its solution if initial position of Z is known Z(0) = x: Give interpretation of the result and the meaning of v and B.
Hint: derive equation for characteristic function, solve it, and then use inverse Fourier transform to obtain P(z; t)
(∂P(z,t))/∂t = -v*(∂P(z,t))/∂z + (B/2)*(∂^2P(z,t))/(∂z^2)
where v and B are constants. Find its solution if initial position of Z is known Z(0) = x: Give interpretation of the result and the meaning of v and B.
Hint: derive equation for characteristic function, solve it, and then use inverse Fourier transform to obtain P(z; t)
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