  The conformational states of a semiflexible polymer enclosed in a compact
domain of typical size $a$ are studied as stochastic realizations of paths
defined by the Frenet equations under the assumption that stochastic
"curvature" satisfies a white noise fluctuation theorem. This approach allows
us to derive the Hermans-Ullman equation, where we exploit a multipolar
decomposition that allows us to show that the positional probability density
function is well described by a Telegrapher's equation whenever
$2a/\ell_{p}>1$, where $\ell_{p}$ is the persistence length. We also develop a
Monte Carlo algorithm for use in computer simulations in order to study the
conformational states in a compact domain. In addition, the case of a
semiflexible polymer enclosed in a square domain of side $a$ is presented as an
explicit example of the formulated theory and algorithm. In this case, we show
the existence of a polymer shape transition similar to the one found by
Spakowitz and Wang [Phys. Rev. Lett. {\bf 91}, 2 (2003)] where in this case the
critical persistence length is $\ell^{*}_{p}\simeq a/8$ such that the
mean-square end-to-end distance exhibits an oscillating behavior for values
$\ell_{p}>\ell^{*}_{p}$, whereas for $\ell_{p}<\ell^{*}_{p}$ it behaves
monotonically increasing.
