  Reconstructing the ancestral state of a group of species helps answer many
important questions in evolutionary biology. Therefore, it is crucial to
understand when we can estimate the ancestral state accurately. Previous works
provide a necessary and sufficient condition, called the big bang condition,
for the existence of an accurate reconstruction method under discrete trait
evolution models and the Brownian motion model. In this paper, we extend this
result to a wide range of continuous trait evolution models. In particular, we
consider a general setting where continuous traits evolve along the tree
according to stochastic processes that satisfy some regularity conditions. We
verify these conditions for popular continuous trait evolution models including
Ornstein-Uhlenbeck, reflected Brownian Motion, and Cox-Ingersoll-Ross.
