  In this paper we consider the Cauchy problem for $2m$-order stochastic
partial differential equations of parabolic type in a class of stochastic
Hoelder spaces. The Hoelder estimates of solutions and their spatial
derivatives up to order $2m$ are obtained, based on which the existence and
uniqueness of solution is proved. An interesting finding of this paper is that
the regularity of solutions relies on a coercivity condition that differs when
$m$ is odd or even: the condition for odd $m$ coincides with the standard
parabolicity condition in the literature for higher-order stochastic partial
differential equations, while for even $m$ it depends on the integrability
index $p$. The sharpness of the new-found coercivity condition is demonstrated
by an example.
