Consider a stochastic process $(X_t:\, t\in\mathbb{Z})$ such that $X_t$ has marginal cdf $F$ for all $t$ and such that the following holds: for all $t$, $x$ and $y$ one has $$ P(X_{t+n}\leq x,\,X_t\leq y) = F(x)F(y) + C(x,y)\alpha^n$$ where $\alpha$ is some universal, positive constant (with $\alpha<1$), and $C$ is some bounded function. Is such a process $\psi$-mixing?
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