Absolute continuity of solutions to the affine stochastic equation
Volume 149 / 2017
Colloquium Mathematicum 149 (2017), 125-136
MSC: Primary 60G30; Secondary 60E10.
DOI: 10.4064/cm6871-7-2016
Published online: 19 May 2017
Abstract
We study local regularity of perpetuities, i.e. solutions $X$ to the stochastic equation $X\overset{d}{=}AX+B$. We give some nontrivial conditions on the law of $(A,B)$ that imply absolute continuity of the law $P_X$ of $X$.
