Stochastic partial differential equations with colored stable noise

We define a random measure generated by certain long-range dependent symmetric $\alpha$-stable random and prove that the measure is $\sigma$-additive in probability. An integral with respect to this measure is constructed, which enables us to consider stochastic partial differential equations, where the random noise has stable distribution and is "coloured". We further study regularity properties of the solution to such equation. The talk is based on the joint research with Larysa Rusanyuk (Pryhara).