Existence, Uniqueness and Tail Behavior of Solutions to Zakai Equations with Unbounded Coefficients

Existence, Uniqueness and Tail Behavior of Solutions to Zakai Equations with Unbounded Coefficients

Title : Existence, Uniqueness and Tail Behavior of Solutions to Zakai Equations with Unbounded Coefficients
Authors :
Blankenship, Gilmer L
Hopkins, William E
Baras, John, S.
Conference : Advances in Filtering and Stochastic Control W.H. Fleming and L.G. Gorostiza Vol. 42 pp. 01-17

Conditions are given to guarantee the existence and uniqueness of solutions to the Duncan-Mortensen-Zakai equation for nonlinear filtering of multivariable diffusions with unbounded coefficients. Sharp upper and lower bounds on the trail of conditional densities are also obtained. A methodology is described to treat these problems using classical p.d.e methods applied to the “robust” version of the DMZ equation. Several examples are included.

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