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Table 1 Selection of analyzed SDEs

From: The Euler scheme for stochastic differential equations with discontinuous drift coefficient: a numerical study of the convergence rate

Drift coefficient Corresponding SDE
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 1 ( , 1.4 ) ( X t )+4 1 [ 1.4 , ) ( X t ))dt+d W t
elementary4minus3 d X t =(4 1 ( , 1.4 ) ( X t )3 1 [ 1.4 , ) ( X t ))dt+d W t
elementary_minus0.6_1 d X t =(0.6 1 ( , 1.4 ) ( X t )+ 1 [ 1.4 , ) ( X t ))dt+d W t
elementary1minus0.6 d X t =( 1 ( , 1.4 ) ( X t )0.6 1 [ 1.4 , ) ( X t ))dt+d W t