We discuss the brane world model of Dvali, Gabadadze and Porrati in which branes evolve in an infinite bulk and the brane curvature term is added to the action. If Z_2 symmetry between the two sides of the brane is not imposed, we show that the model admits the existence of "stealth branes" which follow the standard 4D internal evolution and have no gravitational effect on the bulk space. Stealth branes can nucleate spontaneosly in a Minkowski bulk. This process is described by the standard 4D quantum cosmology formalism with tunneling boundary conditions for the brane world wave function. The notorious ambiguity in the choice of boundary conditions is fixed in this case due to the presence of the embedding spacetime. We also point to some problematic aspects of models admitting stealth brane solutions.

24 pages; Final version, to appear in Phys. Rev. D. The discussion of "embeddability obstruction" is removed (thanks to Takahiro Tanaka who convinced us that there is no such obstruction)