TY - CHAP
T1 - Asymptotic Growth Rates for Exponential Stochastic Growth Processes
AU - Pirjol, Dan
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - This chapter presents the asymptotic theory of the Lyapunov exponents for stochastic growth processes with growth rates proportional to the exponential of a geometric Brownian motion. The Lyapunov exponents of all moments E[(xn)θ] are reduced to two base cases λ±(ρ, β), of the moments θ= ± 1, which are computed explicitly. The Lyapunov exponent λ+(ρ, β) has a phase transition at points along a phase transition curve βtr(ρ).
AB - This chapter presents the asymptotic theory of the Lyapunov exponents for stochastic growth processes with growth rates proportional to the exponential of a geometric Brownian motion. The Lyapunov exponents of all moments E[(xn)θ] are reduced to two base cases λ±(ρ, β), of the moments θ= ± 1, which are computed explicitly. The Lyapunov exponent λ+(ρ, β) has a phase transition at points along a phase transition curve βtr(ρ).
UR - http://www.scopus.com/inward/record.url?scp=85137606949&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85137606949&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-11143-3_6
DO - 10.1007/978-3-031-11143-3_6
M3 - Chapter
AN - SCOPUS:85137606949
T3 - SpringerBriefs in Applied Sciences and Technology
SP - 97
EP - 114
BT - SpringerBriefs in Applied Sciences and Technology
ER -