Problem statement: a continuous wiener process $w(t)$ with unit incremental variance and $w(0)=0$ is given, and then we check the wiener process at every $h$ seconds, $h>0$ is a positive number. If $\left\vert w(kh)\right\vert \geq d$ with $k$ is a positive integer and $d$ is a positive number, then $w(kh)$ is reset to zero. The process continues until $t$ goes to infinite. We want to calculate the variance $ V=\lim_{T\rightarrow \infty }\frac{1}{T}E\int_{0}^{T}w^{2}\left( t\right) dt $
One paper gives the result $V=d^{2}\left( \frac{1}{6}+\frac{5}{6}\frac{h}{h+d^{2}}\right)$ but no details. I want to know how to get this result or the result is correct or not?
Thanks very much for any helps!