Adaptive methods for piecewise linear filtering
A nonlinear discrete-time stochastic dynamical system is considered with piecewise linear drift coefficients and whose initial condition and disturbances are distributed according to finite mixtures of normal distributions. In particular the normal components of the mixtures relative to the state process have variances which vanish with a parameter ε.
For such system the nonlinear filtering problem is studied. It is shown that a suitable linear adaptive filtering problem can be constructed whose solution coincide, for vanishing e, with that of the original nonlinear problem.
The use of measure transformation techniques allows the derivation of the results under milder condition than those assumed so far in a similar context.
KeywordsPiecewise Linear Stochastic Control Polynomial Growth Limit Problem Lebesgue Dominate Convergence Theorem
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