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Theory and Modern Applications

Table 1 Strong and weak solutions for SDEs

From: Stochastic differential equations with singular coefficients on the straight line

b

σ

strong solution

weak solution

continuous

continuous

 

∃

bounded

non-degenerate, continuous

 

∃, unique

bounded

non-degenerate, Lipschitz

∃, unique

 

\(b\in {\mathbb{L}}\)

non-degenerate, \(|\nabla \sigma |\in {\mathbb{L}}\)

∃, unique

 

(1.3)

(1.4)

∃, unique