3 citations · 7 across the 8 of their papers we have counts for
10 papers
Factorization of Time-Ordered Exponentials for Wiener Space Transformations
Jirô Akahori, Takafumi Amaba, Tasuku Kubo
We develop an operator-algebraic framework for change-of-variables formulas on Wiener space, interpreting them as arising from hidden symmetries acting on observables. We show that…
Regularization Effects of Time Integration on Gaussian Process Functionals
Takafumi Amaba, Marie Kratz
In this paper, we investigate the regularization effects, in the sense of Malliavin calculus, on functionals of Gaussian processes induced by time integration, focusing on their co…
Univalence and holomorphic extension of the solution to -controlled Loewner-Kufarev equations
Takafumi Amaba, Roland Friedrich, Takuya Murayama
We prove that a solution to the -controlled Loewner-Kufarev equation, which was introduced by the first two authors, exists uniquely, is univalent and starlike on the unit disk…
Modulus of Continuity of Controlled Loewner-Kufarev Equations and Random Matrices
Takafumi Amaba, Roland Friedrich
First we introduce the two tau-functions which appeared either as the -function of the integrable hierarchy governing the Riemann mapping of Jordan curves or in conformal field…
Controlled Loewner-Kufarev Equation Embedded into the Universal Grassmannian
Takafumi Amaba, Roland Friedrich
We introduce the class of controlled Loewner-Kufarev equations and consider aspects of their algebraic nature. We lift the solution of such a controlled equation to the (Sato)-Sega…
Distributional Itô's Formula and Regularization of Generalized Wiener Functionals
Takafumi Amaba, Yoshihiro Ryu
We investigate Bochner integrabilities of generalized Wiener functionals. We further formulate an Itô formula for a diffusion in a distributional setting, and apply to investigate…
Convergence Implications via Dual Flow Method
Takafumi Amaba, Dai Taguchi, Go Yuki
Given a one-dimensional stochastic differential equation, one can associate to this equation a stochastic flow on , which has an absorbing barrier at zero. Then one c…
A coupling of Brownian motions in the -geometry
Takafumi Amaba, Kazumasa Kuwada
Under a complete Ricci flow, we construct a coupling of two Brownian motion such that their -distance is a supermartingale. This recovers a result of Lott [J. Lott,…
A Discrete-Time Clark-Ocone Formula and its Application to an Error Analysis
Jirô Akahori, Takafumi Amaba, Kaori Okuma
In this paper, we will establish a discrete-time version of Clark(-Ocone-Haussmann) formula, which can be seen as an asymptotic expansion in a weak sense. The formula is applied to…
An Algebraic Approach to the Cameron-Martin-Maruyama-Girsanov Formula
Jiro Akahori, Takafumi Amaba, Sachiyo Uraguchi
In this paper, we will give a new perspective to the Cameron-Martin-Maruyama-Girsanov formula by giving a totally algebraic proof to it. It is based on the exponentiation of the Ma…