2013/05/08 by Eulàlia Nualart, E. Nualart, Nualart, E. +2
Economics, Econometrics and Finance · Mathematics · #28A80 #60G15 #60G17 #60G22 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Probability and Statistical Research #Stochastic processes and financial applications #math.PR #msc:28A80 #msc:60G15 #msc:60G17 #msc:60G22
paper · pdf · doi:10.48550/arxiv.1305.1758
openalex publication_date 2013/05/08 · arxiv created 2014/03/07 · arxiv updated 2014/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a scalar Gaussian process B on ℝ+ with a prescribed general variance function γ2(r) =Var(B(r) ) and a canonical metric E[(B(t) -B(s) ) 2] which is commensurate with γ2(t-s) , we estimate the probability for a vector of d iid copies of B to hit a bounded set A in ℝd, with conditions on γ which place no restrictions of power type or of approximate self-similarity, assuming only that γ is continuous, increasing, and concave, with γ(0) =0 and γ′(0+) =+∞. We identify optimal base (kernel) functions which depend explicitly on γ, to derive upper and lower bounds on the hitting probability in terms of the corresponding generalized Hausdorff measure and non-Newtonian capacity of A respectively. The proofs borrow and extend some recent progress for hitting probabilities estimation, including the notion of two-point local-nondeterminism in Biermé, Lacaux, and Xiao \citeBierme:09.