Geodesic
Robust algorithms of the type of stochastic approximation (continuous time)
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 2, pp. 324-346 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper considers the problem of estimating an unknown drift parameter $\theta$ with observations $yt=\theta+\xi_t$ where $\xi_t$ is a stationary ergodic process. We prove strong consistency and asymptotic normality for the nonlinear estimation of the type of stochastic approximation $$ \hat\theta=\theta_0+\int_0^t\frac{H(y_s-\hat\theta_s)}{(1+s)a_s}\,ds. $$ A method of choosing optimal (in the sense of limit variance) estimation of a function $H$ is offered.
Keywords: nonlinear estimation of a drift parameter, robustness, stochastic approximation. 
@article{TVP_1995_40_2_a6,
     author = {S. V. Lototskii},
     title = {Robust algorithms of the type of stochastic approximation (continuous time)},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {324--346},
     year = {1995},
     volume = {40},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_2_a6/}
}
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S. V. Lototskii. Robust algorithms of the type of stochastic approximation (continuous time). Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 2, pp. 324-346. http://geodesic.mathdoc.fr/item/TVP_1995_40_2_a6/