On the almost sure asymptotic behaviour of stochastic algorithm (Q1807280)

The author considers a stochastic algorithm of the form: \( Z_{n+1}=Z_n +\gamma_n(h(Z_n)+r_n)+ \sigma_n \epsilon_{n+1},\) where \(h :R^d \to R^d,\) \(\{r_n\}\) and \(\{\epsilon_n\}\) are disturbances and \(\{\gamma_n\}\) , \(\{\sigma_n\}\) are nonrandom strictly positive sequences with \(\sum_n\gamma_n<\infty\), \(\sum_n\sigma_n<\infty \). She studies almost sure behavior of the algorithm. A law of iterated logarithm and a quadratic strong law of large numbers are established.