Nonlinear stochastic differential equations and 1/f noise

Connection with other equations
For some choces of parameters our SDE takes the form of well-known
equations.
η = 0 and σ = 1 corresponds to the Bessel process
of dimension δ = 1 − ν
dx = δ − 1
2
1
x dt + dW t
η = 1/2, σ = 2 corresponds to the squared Bessel process
of dimension δ = 2(1 − ν)
dx = δdt + 2 √ x dW t
Julius Ruseckas (Lithuania) Nonlinear stochastic differential equations August 28, 2012 18 / 32