作者：Uchiyama, K
作者单位：Institute of Science Tokyo; Tokyo Institute of Technology
摘要：It is shown that an infinite subset of Z(N) is either recurrent for each aperiodic N-dimensional random walk with mean zero and finite variance, or transient for each of such random walks. This is an exact extension of the result by Spitzer in three dimensions to that in the dimensions N greater than or equal to 4.
作者：Le Gall, JF; Le Jan, Y
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Saclay
摘要：We use the exploration process introduced in a previous work to develop a new construction of superprocesses with a general branching mechanism. This construction depends on a path-valued process called the Levy snake, which is of independent interest. Our method of proof involves a calculation of the Laplace functional of the occupation field of the Levy snake. This calculation relies on an evaluation of the corresponding moment functionals, which requires precise information about the underl...
