Nonlinear stochastic differential equations and 1/f noise
Nonlinear stochastic differential equations and 1/f noise
Nonlinear stochastic differential equations and 1/f noise
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Restriction of diffusion<br />
q-exponential steady-state PDF<br />
dx = σ 2 (η − ν/2)(x + x 0 ) 2η−1 dt + σ(x + x 0 ) η dW t<br />
P 0 (x) ∼ exp 1+1/ν (−νx/x 0 )<br />
Reflective boundary condition at x = 0<br />
q-Gaussian steady-state PDF<br />
dx = σ 2 (η − ν/2)(x 2 + x0 2 )η−1 xdt + σ(x 2 + x0 2 )η/2 dW t<br />
P 0 (x) ∼ exp 1+2/ν (−νx 2 /2x0 2 )<br />
q-exponential function: exp q (x) ≡ (1 + (1 − q)x) 1/(1−q)<br />
J. Ruseckas <strong>and</strong> B. Kaulakys, Phys. Rev. E 84, 051125 (2011).<br />
Julius Ruseckas (Lithuania) <strong>Nonlinear</strong> <strong>stochastic</strong> <strong>differential</strong> <strong>equations</strong> August 28, 2012 17 / 32
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