2018/05/21 by T. Mori, Mori, Takahiro
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1805.07945
openalex publication_date 2018/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider an intersection measure ℓt IS of p independent (possibly different) m-symmetric Hunt processes up to time t in a metric measure space E with a Radon measure m. We derive a Donsker-Varadhan type large deviation principle for the normalized intersection measure t-pℓt IS on the set of finite measures on E as t → ∞, under the condition that t is smaller than life times of all processes. This extends earlier work by W. König and C. Mukherjee (2013), in which the large deviation principle was established for the intersection measure of p independent N-dimensional Brownian motions before exiting some bounded open set D ⊂ ℝN. We also obtain the asymptotic behaviour of logarithmic moment generating function, which is related to the results of X. Chen and J. Rosen (2005) on the intersection measure of independent Brownian motions or stable processes. Our results rely on assumptions about the heat kernels and the 1-order resolvents of the processes, hence include rich examples. For example, the assumptions hold for p∈ ℤ with 2≤ p < p_* when the processes enjoy (sub-)Gaussian type or jump type heat kernel estimates, where p_* is determined by the Hausdorff dimension of E and the so-called walk dimensions of the processes.