Discrete-time Ornstein-Uhlenbeck process in a stationary dynamic environment
نویسندگان
چکیده
We study the stationary solution to the recursion Xn+1 = γXn+ξn, where γ ∈ (0, 1) is a constant and ξn are Gaussian variables with random parameters. Specifically, we assume that ξn = μn + σnεn, where (ε)n∈Z is an i.i.d. sequence of standard normal variables and (μn, σn)n∈Z is a stationary and ergodic process independent of (εn)n∈Z, which serves as an exogenous dynamic environment for the model. JEL codes: C02, C22. MSC2010: primary 60K37, 60G15; secondary 60F05, 62M10.
منابع مشابه
Discrete Ornstein-Uhlenbeck process in a stationary dynamic enviroment
The thesis is devoted to the study of solutions to the following linear recursion: Xn+1 = γXn + ξn, where γ ∈ (0, 1) is a constant and (ξn)n∈Z is a stationary and ergodic sequence of normal variables with random means and variances. More precisely, we assume that ξn = μn + σnεn, where (ε)n∈Z is an i.i.d. sequence of standard normal variables and (μn, σn)n∈Z is a stationary and ergodic process i...
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