The formula of Hölder local exponent is as follows:
$$|f(x)-f(y)| < C.|x-y|^\alpha ,\ \ \ \ \forall\ x,y\in B(x_0,r), $$ $\ C \ constant,$
if $f(x)$ doesn't have a derivative and it is continuous in the same local area centered at $x_0$.
if $f(x)$ have a $p$ derivative $$ |d^pf(x)-d^pf(y)| < C.|x-y|^\alpha $$
How to calculate the local Holder exponent $\alpha(x_0)$ for discrete function (matlab) with DWT wavelet?
Note: point-wise Hölder is calculated in wavelet algorithm with CWT coiflet.. (vanishing moment wavelet), not Hurst Exponent