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 />
Possible forms of restriction:<br />
Reflective boundary conditions at x = x min <strong>and</strong> x = x max<br />
Exponential restriction of the diffusion<br />
dx = σ 2 (<br />
η − ν 2 + m 2<br />
Steady state PDF:<br />
( xmin<br />
x<br />
) m<br />
−<br />
m<br />
2<br />
(<br />
P 0 (x) ∼ x −ν exp −<br />
( xmin<br />
x<br />
( x<br />
x max<br />
) m )<br />
x 2η−1 dt + σx η dW t<br />
) m<br />
−<br />
( x<br />
x max<br />
) m )<br />
Julius Ruseckas (Lithuania) <strong>Nonlinear</strong> <strong>stochastic</strong> <strong>differential</strong> <strong>equations</strong> August 28, 2012 16 / 32