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Results tagged with continuity
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user 99469
2
votes
0
answers
63
views
Construct a differentiable function whose gradient has a prescribed modulus of continuity
We define the following modulus $\psi : \bR_+ \to \bR_+$ of continuity
$$
\psi (x) :=
\begin{cases}
0 &\text{if} \quad x =0 , \\
x | \ln x|^2 &\text{if} \quad x \in (0, \alpha], \\
x - 2 \alpha \ln (\alpha …
- 825
4
votes
Solution of SDE at finite time, continuity of pdf
In Theorem 1.2 of the paper Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift, the authors prove that the transition density of the SDE
$$
\mathrm{d} X_t= …
- 825