The local asymptotic normality of a family of measures generated by solutions of stochastic differential equations with a small fractional Brownian motion. (Ukrainian, English) Zbl 1097.60045

Androshchuk, T.

Teor. Jmovirn. Mat. Stat. 71, 1-14 (2004); translation in Theory Probab. Math. Stat. 71, 1-15 (2005).

The author deals with the stochastic differential equation \(X_{t}=x_0+\int_{0}^{t}S(\theta,u,X_{u})\,du+\varepsilon B_{t}\), \(t\in [0,T]\), where \(x_0\in R\), \(\varepsilon\in(0,1)\); \(S(\theta,u,x)\) is a non-random function; \(\theta\in \Theta\subset R^{d}\) is an unknown parameter; \(B_{t}=B_{t}^{H}\) is a fractional Brownian motion with the Hurst parameter \(H\in(1/2,1)\). He obtains sufficient conditions for the local normality, as \(\varepsilon\to0\), of the family of probability measures \(\{P_{\theta}^{(\varepsilon)}, \theta\in\Theta\}\) generated by solutions of the considered equation.

Reviewer: A. D. Borisenko (Kyïv)

MSC:

60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60F15	Strong limit theorems

Keywords:

system of measures