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The Clark-Ocone formula in the theory of discrete-time chaotic calculus holdsonly for square integrable functionals of discrete-time normal noises. In thispaper, we aim at extending this formula to generalized functionals ofdiscrete-time normal noises. Let $Z$ be a discrete-time normal noise that hasthe chaotic representation property. We first prove a result concerning theregularity of generalized functionals of $Z$. Then, we use the Fock transformto define some fundamental operators on generalized functionals of $Z$, andapply the above mentioned regularity result to prove the continuity of theseoperators. Finally, we establish the Clark-Ocone formula for generalizedfunctionals of $Z$, and show its application results, which include thecovariant identity result and the variant upper bound result for generalizedfunctionals of $Z$.

Clark-Ocone Formula for Generalized Functionals of Discrete-Time Normal Noises