** Classical Model for Super-Brownian Motion**

**Brownian branching particle
systems**

**Empirical measure-valued
processes**

**Multiplicative property and
infinite divisibility**

**MuP is equivalent to
infinite divisibility**

**Log-Laplace functional and
evolution equation**

**Structural properties of
Super-Brownian motion**

**SPDE for Super-Brownian
motion**

**New Model, spatial motion
assumption**

**New Model, branching
mechanism**

**Dependency of the particles
in the new model**

**Loss of the multiplicative
property**

**Construction : existence of
solution of MP**

**Construction : uniqueness of
solution of MP**

**Change the form of the
generator**

**Change the form of the
generator**

**Duality for singular
coefficient**

**Existence of the density
process**

**Feller’s criterion of
accessibility**

**Derivations of SPDEs for
density processes**

**Degenerate SPDE for
purely-atomic superprocess**

**A generalized new model and
SDSM**

**New Model, spatial motion
assumption**

**New Model, branching
mechanism**

**Dependency of the particles
in the new model**

**Construction : existence of
solution of MP**

**State classification for
this location dependent branching model**