Conditions for Stationarity and Ergodicity of Two-factor Affine Diffusions

Abstract

Sufficient conditions are presented for the existence of a unique stationary distribution and exponential ergodicity of two-factor affine diffusion processes.

On conditional least squares estimation for affine diffusions based on continuous time observations

“…. , ⌊nT ⌋}, the distribution of (Y i−1 n , X i−1 n ) is absolutely continuous, because, as in the proof of part (b) in the proof of Theorem A.1 in Bolyog and Pap [11], the conditional distribution of (…”

“…which happens with probability 0, since x = (x 1 , x 2 , x 3 ) ⊤ = 0 and, for each s ∈ (0, T ], the distribution of (Y s , X s ) is absolutely continuous, because, as in the proof of part (b) in the proof of Theorem A.1 in Bolyog and Pap [11], the conditional distribution of (Y s , X s ) given (Y 0 , X 0 ) is absolutely continuous.…”

“…where A := α − ra, B := β − r(b − γ) and Σ 2 := σ 2 1 − ̺ 2 , see Bolyog and Pap [11,Proposition 2.5]. We have…”

“…The following result states the existence of a unique stationary distribution of the affine diffusion process given by the SDE (1.1), see Bolyog and Pap [11,Theorem 3.1]. Let C − := {z ∈ C : Re(z) 0}.…”

“…In the subcritical case, the following result states the exponential ergodicity and a strong law of large numbers for the process (Y t , X t ) t∈R + , see Bolyog and Pap [11,Theorem 4.1].…”