Nonlinear stochastic differential equations and 1/f noise

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