Nonlinear stochastic differential equations and 1/f noise

Connection with other equations
SDE with exponential restriction with η = 1/2, x min = 0 and m = 1
gives Cox-Ingersoll-Ross (CIR) process
dx = k(θ − x)dt + σ √ x dW t
where k = σ 2 /2x max , θ = x max (1 − ν)
When ν = 2η, x max = ∞ and m = 2η − 2 then we get the
Constant Elasticity of Variance (CEV) process
where µ = σ 2 (η − 1)x 2(η−1)
min
dx = µxdt + σx η dW t
Julius Ruseckas (Lithuania) Nonlinear stochastic differential equations August 28, 2012 19 / 32