Simulation of conditional diffusions via forward-reverse stochastic representations


Bayer, Christian


We derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval,conditioned on the terminal state. The conditioning can be with respect to a fixed measurement point or more generally with respect to some subset. The representations rely on a reverse process connected with the given (forward) diffusion as introduced by Milstein, Schoenmakers and Spokoiny in the context of density estimation. The corresponding Monte Carlo estimators have essentially root-N accuracy, and hence they do not suffer from the curse of dimensionality. We also present an application in statistics, in the context of the EM algorithm.

Conference/Event Name
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

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