I was reading a physical textbook and they used the "Stratonovich product" referred to $v_1 \circ dW_1 = \frac{1}{2}[v_1 + (v_1+dv_1)]dW_1$. I think this product is from the Stochastic process, thus Stratonovich integral, but I'm not sure how the product of $v_1 \circ dW_1$ reduces to such simple formula. Is anyone can help me to figure out what's going on?
The textbook made a reference as following book "C. Gardiner, Stochastic Methods, A Handbook for the Natural and Social Sciences (Springer, New York, 2010)." Though I borrowed this book from library and looked over it, but I still don't grasp what's going on. Thanks!