Daniel Altemeier (Dipl. Wirt.-Math.)
- Default value: \(A=0.7,~ \nu=0.1,~ \sigma=0.05,~ \beta= 0.5,~ \epsilon^{-1}=1\),
\[dx_t = -\nabla V(x_t)dt + \beta \nabla U(x_{t-r}) dt + A\cos\left(2\pi \nu t\right)dt + \sqrt{\sigma}dW_t\]
For \( \epsilon>0 \), time transformation \( s=\epsilon t \) yields
\[
d\tilde{x}_s = -\frac{1}{\epsilon}\nabla V(\tilde{x}_s)ds + \frac{1}{\epsilon}\beta \nabla U(\tilde{x}_{s-\epsilon r}) ds + \frac{A}{\epsilon}\cos\left(\frac{2\pi\nu}{\epsilon}s\right)ds + \sqrt{\frac{\sigma}{\epsilon}}d\tilde{W}_s.
\]
