Polylinear additive functionals of superprocesses
The author has already studied the linear additive functionals of superprocesses in a previous work [Trans. Am. Math. Soc. 314, No. 1, 255-282 (1989; Zbl 0674.60070)]. But the study of self-intersection local times and \(k\)-multiple points of superprocesses raised the question of polylinear additive functionals. If \(X\) is a superdiffusion in a domain \(E\) of \(\mathbb{R}^d\), a polylinear additive functional of \(X\) corresponding to a positive Borel function \(\rho\) on \((\mathbb{R}_+\times E)^k\) is given by integrating \(\rho\) with respect to the kernel \(X_{t_1}(dz_1)\otimes\cdots\otimes X_{t_k}(dz_k)\), and a general polylinear additive functional is obtained by a passage to the limit from functionals of the previous form. The properties of such functionals are investigated, and an application to self-intersection local times of order \(k\) is given.
scientific article; zbMATH DE number 1054131
scientific article