  We consider a stochastic search model with resetting for an unknown
stationary target $a\in\mathbb{R}^d,\ d\ge1$, with known distribution $\mu$.
The searcher begins at the origin and performs Brownian motion with diffusion
coefficient $D$. The searcher is also armed with an exponential clock with rate
$r>0$, so that if it has failed to locate the target by the time the clock
rings, then its position is reset to the origin and it continues its search
anew from there. In dimension one, the target is considered located when the
process hits the point $a$, while in dimensions two and higher, one chooses an
$\epsilon_0>0$ and the target is considered located when the process hits the
$\epsilon_0$-ball centered at $a$.
  Denote the position of the searcher at time $t$ by $X(t)$, let $\tau_a$
denote the time that a target at $a$ is located, and let $P^{d;(r,0)}_0$ denote
probabilities for the process starting from 0. Taking a functional analytic
point of view, and using the generator of the Markovian search process and its
adjoint, we obtain precise estimates, uniformly in $a$, on the asymptotic
behavior of $P^{d;(r,0)}_0(\tau_a>t)$ for large time, and then use this to
obtain large time estimates on
$\int_{\mathbb{R}^d}P^{d;(r,0)}_0(\tau_a>t)d\mu(a)$, the probability that the
searcher has failed up to time $t$ to locate the random target, distributed
according to $\mu$.
