This paper concerns the filtering problem for a class of continuous-time Markovian jump linear systems, where the Markovian jump is supposed to frequently occur in some short time intervals. For this class of Markovian jump system, the boundedness of estimation error deserves our investigation. By introducing the concepts of stochastic boundedness with respect to a finite-time interval, an observer ensuring the estimation error bounded in a prescribed boundary is constructed and the result is extended to the H filtering problem with norm bounded disturbances. By formulating an optimization algorithm, we derive the optimal H stochastic boundedness filter with an an optimized convex combination of estimation error boundary and H performance index. We propose a design algorithm for when parameter optimization is involved. Numerical design examples are given to illustrate the effectiveness of our results.