Dalang, Robert C.Humeau, Thomas2019-07-072019-07-072019-07-072019-01-0110.1214/19-EJP317https://infoscience.epfl.ch/handle/20.500.14299/158907WOS:000472652800001We study the notions of mild solution and generalized solution to a linear stochastic partial differential equation driven by a pure jump symmetric Levy white noise, with symmetric alpha-stable Levy white noise as an important special case. We identify conditions for existence of these two kinds of solutions, and, together with a new stochastic Fubini theorem, we provide conditions under which they are essentially equivalent. We apply these results to the linear stochastic heat, wave and Poisson equations driven by a symmetric alpha-stable Levy white noise.Statistics & ProbabilityMathematicslinear stochastic partial differential equationlevy white noisegeneralized stochastic processmild solutionstochastic fubini theoremalpha-stable noisetext::journal::journal article::research article