The heat equation with Lévy noise1

Athreya K.B., Ney, P.E., 1972. Branching Processes. Springer Berlin. Dawson D.A., 1993. Measure-valued Markov processes. In P.L. Hennequin, (ed.), Ecole d’Ete de Probabilites de Saint Flour XXI-1991, Lecture Notes in Mathematics Springer, Berlin. Ito K., 1961. Lectures on Stochastic Processes. Tata Institute of Fundamental Research, Bombay, Konno, 1988, Stochastic partial differential equations for some measure-valued diffusions, Probab. Theory Rel. Fields, 79, 201, 10.1007/BF00320919 Lamperti, 1967, Continuous state branching processes, Bull. Amer. Math. Soc., 73, 382, 10.1090/S0002-9904-1967-11762-2 Mueller, 1991, Long time existence for the heat equation with a noise term, Probab. Theory Related Fields, 90, 505, 10.1007/BF01192141 Neveu J., A continuous state branching process in relation with the grem model of spin glasses theory. Preliminary version, 1992. Rosinski, 1986, On Ito stochastic integration with respect top-stable motion:inner clock, integrability of sample paths, double and multiple integrals, Ann. Probab., 14, 271, 10.1214/aop/1176992627 Walsh J.B., 1986 An introduction to stochastic partial differential equations. In P. L. Hennequin, (ed.), Ecole d’Ete de Probabilites de Saint Flour XIV-1984, Lecture Notes in Math. 1180 Springer, Berlin. Watanabe, 1968, A limit theorem of branching processes and continuous state branching processes, J. Math. Kyoto U., 3, 141