The paper presents an algorithm to solve goal-directed path planning problems in dynamic and uncertain environments. A grid-based path planning algorithm, called ν*, was formulated in the framework of probabilistic finite state automata (PFSA) from a control-theoretic perspective. The work reported in this paper extends the formulation of path planning in environments with static obstacles to include the presence of dynamic obstacles with stochastic motion models. The framework to solve this problem involves an initial plan that is based on the time-averaged likelihood of dynamic obstacles being present at a particular location. This information is inferred from the stochastic model. Additionally, there is a path re-planning component, based on the current measurements. Results of numerical simulation are presented to demonstrate the efficacy of the proposed concept.