ProV Logo
0
Long-run growth rate in a random multipl...
Pirjol, Dan...

Free

Long-run growth rate in a random multiplicative model by Pirjol, Dan ( Author )
Lemonjar Open Access
N.A
07-03-2015
We consider the long-run growth rate of the average value of a random multiplicative process xi+1=aixi where the multipliers ai=1+ρexp(σWi−12σ2ti) have Markovian dependence given by the exponential of a standard Brownian motion Wi. The average value ⟨xn⟩ is given by the grand partition function of a one-dimensional lattice gas with two-body linear attractive interactions placed in a uniform field. We study the Lyapunov exponent λ(ρ,β)=limn→∞1nlog⟨xn⟩ at fixed β=12σ2tnn, and show that it is given by the equation of state of the lattice gas in thermodynamical equilibrium. The Lyapunov exponent has discontinuous first derivatives along a curve in the (ρ,β) plane ending at a critical point (ρC,βC), which is related to a phase transition in the equivalent lattice gas. Using the equivalence of the lattice gas with a bosonic system, we obtain the exact solution for the equation of state in the thermodynamical limit n→∞.
-
Article
pdf
36.88 KB
English
-
MYR 0.01
-
https://arxiv.org/abs/1503.02168
Share this eBook