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Publication - Dr Mathieu Gerber

    Stability with respect to initial conditions in V-norm for nonlinear filters with ergodic observations

    Citation

    Gerber, M & Whiteley, N, 2017, ‘Stability with respect to initial conditions in V-norm for nonlinear filters with ergodic observations’. Journal of Applied Probability, vol 54., pp. 118-133

    Abstract

    We establish conditions for an exponential rate of forgetting of the initial distribution of nonlinear filters in V-norm, allowing for unbounded test functions. The analysis is conducted in an general setup involving nonnegative kernels in a random environment which allows treatment of filters and prediction filters in a single framework. The main result is illustrated on two examples, the first showing that a total variation norm stability result obtained by Douc et al. (2009) can be extended to V-norm without any additional assumptions, the second concerning a situation in which forgetting of the initial condition holds in V-norm for the filters, but the V-norm of each prediction filter is infinite.

    Full details in the University publications repository