  Stochastic processes wherein the size of the state space is changing as a
function of time offer models for the emergence of scale-invariant features
observed in complex systems. I consider such a sample-space reducing (SSR)
stochastic process that results in a random sequence of strictly decreasing
integers $\{x(t)\}$, $0\le t \le \tau$, with boundary conditions $x(0) = N$ and
$x(\tau)$ = 1. This model is shown to be exactly solvable:
$\mathcal{P}_N(\tau)$, the probability that the process survives for time
$\tau$ is analytically evaluated. In the limit of large $N$, the asymptotic
form of this probability distribution is Gaussian, with mean and variance both
varying logarithmically with system size: $\langle \tau \rangle \sim \ln N$ and
$\sigma_{\tau}^{2} \sim \ln N$. Correspondence can be made between survival
time statistics in the SSR process and record statistics of i.i.d. random
variables.
