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Are differentials on their own in stochastic calculus just an abuse of notation?

Differentials in stochastic calculus have very precise interpretations. The stochastic differential equation in differential form $$dX_t = \mu (t, X_t) dt + \sigma (t, X_t) dB_t$$ translates precisely ...
Jose Avilez's user avatar
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How to prove an adapted Feynman Kac Formula for $v_t + \frac{1}2 \sigma ^2 (t,y) v_{yy} + b(t,y) v_y - \delta(t,y) v + h(y) = 0$ using SDE techniques?

We see $$\begin{aligned}dv(t,Y_t)-\delta(t,Y_t)v(t,Y_t)dt&=-h(Y_t)dt+v_y(t,Y_t)\sigma(t,Y_t)dW_t\\ \implies d(v(t,Y_t)e^{-\int_0^t\delta(s,Y_s)ds})&=-h(Y_t)e^{-\int_0^t\delta(s,Y_s)ds}dt+v_y(t,...
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