Table 1 Selection of analyzed SDEs

sign

\(dX_{t} = \operatorname{sgn}(X_{t})\,dt + dW_{t}\)

minusSign

\(dX_{t} = -\operatorname{sgn}(X_{t})\,dt + dW_{t}\)

10sign

\(dX_{t} = 10 \cdot \operatorname{sgn}(X_{t})\,dt + dW_{t}\)

minus10sign

\(dX_{t} = -10 \cdot \operatorname{sgn}(X_{t})\,dt + dW_{t}\)

elementary_minus34

$d{X}_t=(-3\cdot {\mathbb{1}}_{(-\mathrm{\infty },1.4)}(X_t)+4\cdot {\mathbb{1}}_{[1.4,\mathrm{\infty })}(X_t))dt+d{W}_t$

elementary4minus3

$d{X}_t=(4\cdot {\mathbb{1}}_{(-\mathrm{\infty },1.4)}(X_t)-3\cdot {\mathbb{1}}_{[1.4,\mathrm{\infty })}(X_t))dt+d{W}_t$

elementary_minus0.6_1

$d{X}_t=(-0.6\cdot {\mathbb{1}}_{(-\mathrm{\infty },1.4)}(X_t)+{\mathbb{1}}_{[1.4,\mathrm{\infty })}(X_t))dt+d{W}_t$

elementary1minus0.6

$d{X}_t=({\mathbb{1}}_{(-\mathrm{\infty },1.4)}(X_t)-0.6\cdot {\mathbb{1}}_{[1.4,\mathrm{\infty })}(X_t))dt+d{W}_t$