  There are certain classes of resistors, capacitors and inductors that, when
subject to a periodic input of appropriate frequency, develop hysteresis loops
in their characteristic response. Here, we show that the hysteresis of such
memory elements can also be induced by white noise of appropriate intensity
even at very low frequencies of the external driving field. We illustrate this
phenomenon using a physical model of memory resistor realized by
$\mathrm{TiO_2}$ thin films sandwiched between metallic electrodes, and discuss
under which conditions this effect can be observed experimentally. We also
discuss its implications on existing memory systems described in the literature
and the role of colored noise.
