I am having trouble with the following passage on Ikeda and Watanabe (Stochastic Differential equations and Diffusion processes - page 173-174)
The theorem that he cites is
In this case shouldn't we arrive (in the display of pg 174) at
$$w(t) = x + \int_0^t \sigma_m (w(s))\, dB_s$$ where $$\sigma_m (w(s)) = \sigma(Y_m(w))$$
Is this indeed a typo or am I missing something?