21 citations · 39 across the 12 of their papers we have counts for
13 papers
Asymptotics of lowlying Dirichlet eigenvalues of Witten Laplacians on domains in pinned path groups
Shigeki Aida
Let be a compact connected Lie group and be the pinned path space with a pinned Brownian motion measure defined by the heat k…
An interpolation of discrete rough differential equations and its applications to analysis of error distributions
Shigeki Aida, Nobuaki Naganuma
We consider the solution and several approximate solutions of a rough differential equation driven by a fractional Brownian motion with th…
Error analysis for approximations to one-dimensional SDEs via the perturbation method
Shigeki Aida, Nobuaki Naganuma
We study asymptotic error distributions associated with standard approximation scheme for one-dimensional stochastic differential equations driven by fractional Brownian motions. T…
Rough differential equations containing path-dependent bounded variation terms
Shigeki Aida
We consider rough differential equations whose coefficients contain path-dependent bounded variation terms and prove the existence and a priori estimate of solutions. These equatio…
Reflected rough differential equations via controlled paths
Shigeki Aida
In [1], we proved the existence of solutions to reflected rough differential equations based on an idea of Euler approximation of the solutions which is due to Davie [6]. In this p…
Asymptotics of spectral gaps on loop spaces over a class of Riemannian manifolds
Shigeki Aida
We prove the existence of spectral gaps of Ornstein-Uhlenbeck operators on loop spaces over a class of Riemannian manifolds which include hyperbolic spaces. This is an alternative…