Stochastic motions of the two-dimensional many-body delta-Bose gas, IV: Transformations of relative motions

This paper is the last in a series devoted to constructing stochastic motions representing the two-dimensional $N$-body delta-Bose gas for all integers $N\ge 3$ via Feynman-Kac-type formulas. The main result here supplements [1,2] of the series by proving a bijective transformation between two general classes of Langevin-type SDEs such that the SDEs of one class describe precisely the stochastic relative motions of the SDEs of the other class.