.png){kind=icon}
.png){kind=icon}
Return
Exit time analysis for Kesten's stochastic recurrence equations
.png){kind=icon}
PRE
AI
R
R
S
DOI：10.1007/s00440-025-01461-x.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
Kesten's stochastic recurrent equation is a classical subject of research in probability theory and its applications. Recently, it has garnered attention as a model for stochastic gradient descent with a quadratic objective function and the emergence of heavy-tailed dynamics in machine learning. This context calls for analysis of its asymptotic behavior under both negative and positive Lyapunov exponents. This paper studies the exit times of the Kesten's stochastic recurrence equation in both cases. Depending on the sign of Lyapunov exponent, the exit time scales either polynomially or logarithmically as the radius of the exit boundary increases.
Keywords:
REVERSIBLE DIFFUSION-PROCESSES
METASTABILITY
ASYMPTOTICS
PRODUCTS
DYNAMICS
FIELD
Journal
P
IF:
1.6
Papers:
61
Citations:
0
Organization
Cited Papers