  We propose an intermediate walk continuously connecting an open quantum
random walk and a quantum walk with parameters $M\in \mathbb{N}$ controlling a
decoherence effect; if $M=1$, the walk coincides with an open quantum random
walk, while $M=\infty$, the walk coincides with a quantum walk. We define a
measure which recovers usual probability measures on $\mathbb{Z}$ for
$M=\infty$ and $M=1$ and we observe intermediate behavior through numerical
simulations for varied positive values $M$. In the case for $M=2$, we
analytically show that a typical behavior of quantum walks appears even in a
small gap of the parameter from the open quantum random walk. More precisely,
we observe both the ballistically moving towards left and right sides and
localization of this walker simultaneously. The analysis is based on Kato's
perturbation theory for linear operator. We futher analyze this limit theorem
in more detail and show that the above three modes are described by Gaussian
distributions.
