On the quasi-everywhere existence of the local time of the solution of a stochastic differential equation (Q1917792)

Let \(Y_t= x_0+\int^t_0\sigma(Y_s)dB_s+ \int^t_0b(Y_s)ds\) be a one-dimensional stochastic differential equation with coefficients \(b,\sigma\in C^2_b(\mathbb{R})\) and driving Brownian motion. The author proves the quasi-everywhere existence (the existence except for a set of zero capacity) of the local time of the solution \(Y\) provided either \(\sigma\) is uniformly positive or \(b=0\).