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This paper presents an action functional, sample path optimization technique, for formulating and solving nonlinear discrete-time stochastic H∞ estimation problems. These H∞ problems are formulated as minimax dynamic games in which the maximizing players are stochastic square summable disturbances, while the minimizing players are the state estimates. Certain action functionals are defined which play the role of information state and its adjoint in converting the minimax game into a fully observable game. Subsequently, a verification theorem is derived.