Conditioned superprocesses and a semilinear heat equation
Measure-valued branching processes (hereafter called MVB processes and denoted Xt) have been the subject of intensive study over the last twenty years. We recommend Dawson  as an excellent general reference and for the rest of this note assume some familiarity with the construction and characterisation of these processes. We shall be concerned only with the special case when the branching mechanism has finite variance and the MVB process takes its values in M F(E) (finite measures on a Polish space E). In particular we will be motivated by a pathwise construction of the MVB process due to Le Gall .
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