Nonparametric estimation of linear multiplier for SDEs driven by generalized stochastic volatility

arXiv:2412.00005v2 Announce Type: replace Abstract: We study the problem of nonparametric estimation of the linear multiplier function $\theta(t)$ for processes satisfying stochastic differential equations of the type $$dX_t= \theta(t)X_t dt+ \epsilon\; \sigma(t,X_t,Y_t)dW_t, X_0=x_0, 0 \leq t \leq T$$ based on the observation of the process $\{X_t, 0\leq t \leq T\}$ and investigate the asymptotic properties of the estimator as the small noise $\epsilon$ tends to zero. Here $\{W_t, t\geq 0\}$ is the standard Brownian motion and $\{Y_t, t\geq 0\}$ is a process adapted to the filtration generated by the Brownian motion.