Sharp barrier estimates for Bessel bridges

2025/11/17 by Leandro Chiarini, Chiarini, Leandro, Ellen Powell +1
Economics, Econometrics and Finance · Mathematics · #60G40 #60J60 #60J65 #Advanced Harmonic Analysis Research #FOS: Mathematics #Geometry and complex manifolds #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2511.13416

openalex publication_date 2025/11/17 · openalex created_date 2025/11/19 · openalex updated_date 2026/07/28

Abstract

In this article, we derive precise estimates for the probability that a Bessel bridge of dimension d ≥ 0 and end points x and a+bT-j stays below the linear barrier a + bt for all t ∈ [0,T]. We identify the leading order term as well as the asymptotic error for this probability as T→ ∞, depending on a,b,j,x. We also derive the behaviour of such leading term as we allow a,j→ ∞, and obtain precise bounds for all error terms. Finally, we establish a complementary result where the linear barrier is perturbed by a small concave function.

Citations

• The kernel method for lattice paths below a line of rational slope
• Convergence in law of the maximum of nonlattice branching random walk
• On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes
• Tightness of the recentered maximum of the two-dimensional discrete Gaussian Free Field
• Ballot theorems for random walks with finite variance

Related

• Bessel SPDEs and renormalised local times
• Taylor Estimates for the laws of pinned Bessel bridges, and Integration by Parts
• On the weak convergence of conditioned Bessel bridges
• Bessel SPDEs with general Dirichlet boundary conditions
• On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes