Question: Show that Remark 22.5.a) remains valid if we replace (f(x)) by (f(s, x)). 22.5 Remark. a) The Stratonovich integral satisfies the classical chain rule. Indeed,
Show that Remark 22.5.a) remains valid if we replace \(f(x)\) by \(f(s, x)\).
22.5 Remark. a) The Stratonovich integral satisfies the classical chain rule. Indeed, if fe e(R) and dX = (t) dB + b(t) dt is an It process, we get (18.13) df(x+) f'(x+) dx++ " (X+) (dx+) = = f'(x)o(t) dB +f'(x)b(t) dt +f" (X)o(t) dt (227) f'(x)o(t) dB + f'(x)b(t) dt = f'(xt) odXt,
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