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Absolute continuity of solutions to the affine stochastic equation

Volume 149 / 2017

Witold Świątkowski 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 $X$.

Authors

  • Witold ŚwiątkowskiInstitute of Mathematics
    University of Wrocław
    50-384 Wrocław, Poland
    e-mail

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