Generators of feller semigroups with coefficients depending on parameters and optimal estimators


We consider the realization of the operator Lθ,au(x):= x2au″(x) + (ax2a-1 + θxa) u′(x), acting on C[O, +∞], for θ ε®, a ε®. We show that Lθ,a, with the so called Wentzell boundary conditions, generates a Feller semigroup for any θ ε ®, a ε ®. The problem of finding optimal estimators for the corresponding diffusion processes is also discussed, in connection with some models in financial mathematics. Here C[0, +∞] is the space of all real valued continuous functions on [0, +∞) which admit finite limit at +∞.

Publication Title

Discrete and Continuous Dynamical Systems - Series B

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