Consider a class of densities that are piecewise constant functions over partitions of the sample space defined by sequential coordinate partitioning. We introduce a prior distribution for a density in this function class and derive in closed form the marginal posterior distribution of the...

A joint large deviation principle for G-Brownian motion and its quadratic variation process is presented. The rate function is not a quadratic form due to quadratic variation uncertainty. A large deviation principle for stochastic differential equations driven by G-Brownian motion is also...