ABSTRACT
We consider a parametrized family of NLSS with parameter space https://www.w3.org/1998/Math/MathML"> Θ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429112638/a69a2ff5-a02c-4831-8fae-bdc86f3c20b4/content/eq12863.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . For each parameter https://www.w3.org/1998/Math/MathML"> θ ∈ Θ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429112638/a69a2ff5-a02c-4831-8fae-bdc86f3c20b4/content/eq12864.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , the distribution of the NLSS is specified by the transition kernel https://www.w3.org/1998/Math/MathML"> M θ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429112638/a69a2ff5-a02c-4831-8fae-bdc86f3c20b4/content/eq12865.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> of the underlying Markov chain https://www.w3.org/1998/Math/MathML"> X t , t ∈ N https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429112638/a69a2ff5-a02c-4831-8fae-bdc86f3c20b4/content/eq12866.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , and by the conditional density https://www.w3.org/1998/Math/MathML"> g θ X t , Y t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429112638/a69a2ff5-a02c-4831-8fae-bdc86f3c20b4/content/eq12867.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> of the observation https://www.w3.org/1998/Math/MathML"> Y t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429112638/a69a2ff5-a02c-4831-8fae-bdc86f3c20b4/content/eq12868.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> given the state https://www.w3.org/1998/Math/MathML"> X t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429112638/a69a2ff5-a02c-4831-8fae-bdc86f3c20b4/content/eq12869.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> with respect to some dominating measure https://www.w3.org/1998/Math/MathML"> μ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429112638/a69a2ff5-a02c-4831-8fae-bdc86f3c20b4/content/eq12870.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> .
