Adaptive prediction and reverse martingales

Tomas Bjork and Björn Johansson

Stochastic Processes and their Applications, 1992, vol. 43, issue 2, 191-222

Abstract: We study prediction problems for models where the underlying probability measure is not known. These problems are intimately connected with time reversal of Markov processes, and optimal predictors are shown to be characterized by being reverse martingales. For a class of diffusions we give a Feynman-Kac representation of the optimal predictor in terms of an associated complex valued diffusion and a concrete Wiener model is studied in detail. We also derive Cramér-Rao inequalities for the prediction error.

Keywords: prediction; time; reversal; martingales; diffusions; point; processes; information; inequalities (search for similar items in EconPapers)
Date: 1992
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Citations: View citations in EconPapers (3)

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