How to Apply Statistical Algorithms of Signal Processing to Regulate Variation of a Curve?
You can regulate its second derivative which is the curvature.

Something like:

$$ \hat{x} = \arg \min_{x} \frac{1}{2} \left\| x - y \right\|_{2}^{2} + \frac{\lambda}{2} \left\| D D x \right\|_{2}^{2}  $$

Where $ y $ is samples you have and $ D $ is the Derivative Operator (In Matrix Form). By applying it twice we're regulating the Second Derivative.
You can find a statistical explanation for this (Prior of Gaussian Distribution of the Second Derivative) or just call is Tikhonov Regularization.

This has a closed form solution:

$$ \hat{x} = \left( I + \lambda {D}^{T} {D}^{T} D D \right)^{-1} y $$