A limit theorem for stochastic equations with the local time (Q2771529)

This paper deals with necessary and sufficient conditions for weak convergence as \(\varepsilon \to 0\) of solutions of the stochastic equation NEWLINE\[NEWLINE\xi_{\varepsilon}(t)=x+b_{\varepsilon}L^{\xi_{\varepsilon}}(t,0)+ \int_0^t g_{\varepsilon}(\xi_{\varepsilon}(s)) ds+ \int_0^t\sigma_{\varepsilon}(\xi_{\varepsilon}(s)) dW(s),NEWLINE\]NEWLINE where \(W(s)\) is a standard Brownian motion, \(g_{\varepsilon}(\cdot)\) and \(\sigma_{\varepsilon}(\cdot)\) are non-random functions, \(L^{\xi_{\varepsilon}}(t,0)\) is a symmetric local time of the process \(\xi_{\varepsilon}\) in zero defined by Tanaka's formula.