Geodesic
Comparison of linear and nonlinear filtration of some Markov processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 3, pp. 528-533

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Let ($\theta_t,\eta_t$) be a two-dimensional Markov process where $\theta_t$ is a homogeneous Markov process with two states and $\eta_t$ satisfies equation (1). We solve the problem of filtration (linear and nonlinear) of the process $\theta_t$ under the condition that it is possible to observe $\eta_t$. The results of comparison of the linear and nonlinear filtration are given. 
@article{TVP_1966_11_3_a14,
     author = {R. Sh. Liptser},
     title = {Comparison of linear and nonlinear filtration of some {Markov} processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {528--533},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {1966},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1966_11_3_a14/}
}
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R. Sh. Liptser. Comparison of linear and nonlinear filtration of some Markov processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 3, pp. 528-533. http://geodesic.mathdoc.fr/item/TVP_1966_11_3_a14/