State Space Model with Random Walk State Equation

[workhard]

Dear all,

I wish to produce time-varying coefficients by using state space model & assumed the state variables (the time-varying coefficients) to follow a random walk process. That is:
@signal y = sv1+ sv2*x + [var = exp(c(1))]
@state sv1 = sv1(-1) + [var = exp(c(2))]
@state sv2 = sv2(-1) + [var = exp(c(3))]

However, when I perform unit root test on the sv1 series, the result shows that the sv1 series is stationary.
May I know why the non-stationary random walk process can produce stationary sv1 series?
Is it make sense?

Can anyone explain to me what is the reason behind or suggest related references to me.

Any prompt reply is greatly appreciated.
Thanks..