New answers tagged stochastic-differential-equations
1
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Is there a way to solve linear 1st order ODEs with time-varying coefficients driven by geometric Brownian motion?
It really depends on what you mean by $c(t) X_t$. The natural approach here, as mentioned in the answer by @Abezhiko, is to solve an ODE for each trajectory (path) of the geometric Brownian Motion. ...
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8
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Is there a way to solve linear 1st order ODEs with time-varying coefficients driven by geometric Brownian motion?
Since the stochastic process $X_t$ appears only in the source term, you can solve this differential equation with respect to $y(t)$ as usual, hence
$$
y(t) = y(0)e^{F(t)} - \int_0^t \frac{c(s)}{a(s)} ...
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