54 citations · 114 across the 25 of their papers we have counts for
30 papers
Sub-Riemannian spectral distance
Yuzuru Inahama
We study eigenvalues and eigenfunctions of the ``div-grad type" sub-Laplacian with respect to Popp's volume on a compact equiregular sub-Riemannian manifold . Since Popp's volum…
Fractional Diffusion Bridges
Yuzuru Inahama
Consider ``stochastic differential equations" driven by fractional Brownian motion with Hurst parameter H (1/4 <H< 1). Their solutions are sometimes called fractional diffusion pro…
Averaging principle for rough slow-fast systems of level 3
Yuzuru Inahama
The averaging principle for slow-fast systems of various kind of stochastic (partial) differential equations has been extensively studied. An analogous result was shown for slow-fa…
Moderate deviations for two-time scale systems with mixed fractional Brownian motion
Xiaoyu Yang, Yuzuru Inahama, Yong Xu
This work focuses on moderate deviations for two-time scale systems with mixed fractional Brownian motion. Our proof uses the weak convergence method which is based on the variatio…
Moderate deviations for rough differential equations
Yuzuru Inahama, Yong Xu, Xiaoyu Yang
Small noise problems are quite important for all types of stochastic differential equations. In this paper we focus on rough differential equations driven by scaled fractional Brow…
Wong-Zakai approximation of density functions
Yuzuru Inahama
In this paper we prove the Wong-Zakai approximation of probability density functions of solutions at a fixed time of rough differential equations driven by fractional Brownian roug…
Large deviation principle for slow-fast system with mixed fractional Brownian motion
Yuzuru Inahama, Yong Xu, Xiaoyu Yang
This work focuses on a slow-fast system perturbed by mixed fractional Brownian motion with Hurst parameter . The integral with respect to fractional Brownian motion is…
Support theorem for pinned diffusion processes
Yuzuru Inahama
In this paper we prove a support theorem of Stroock-Varadhan type for pinned diffusion processes. To this end we use two powerful results from stochastic analysis. One is quasi-sur…
Averaging principle for slow-fast systems of rough differential equations via controlled paths
Yuzuru Inahama
In this paper we prove the strong averaging principle for a slow-fast system of rough differential equations. The slow and the fast component of the system are driven by a rather g…
Large deviations for small noise hypoelliptic diffusion bridges on sub-Riemannian manifolds
Yuzuru Inahama
In this paper we study a large deviation principle of Freidlin-Wentzell type for pinned hypoelliptic diffusion measures associated with a natural sub-Laplacian on a compact sub-Rie…
Averaging principle for fast-slow system driven by mixed fractional Brownian rough path
Bin Pei, Yuzuru Inahama, Yong Xu
This paper is devoted to studying the averaging principle for fast-slow system of rough differential equations driven by mixed fractional Brownian rough path. The fast component is…
Positivity of the density for rough differential equations
Yuzuru Inahama, Bin Pei
Due to recent developments of Malliavin calculus for rough differential equations, it is now known that, under natural assumptions, the law of a unique solution at a fixed time has…
Pathwise unique solutions and stochastic averaging for mixed stochastic partial differential equations driven by fractional Brownian motion and Brownian motion
Bin Pei, Yuzuru Inahama, Yong Xu
This paper is devoted to a system of stochastic partial differential equations (SPDEs) that have a slow component driven by fractional Brownian motion (fBm) with the Hurst paramete…
Averaging Principles for Mixed Fast-Slow Systems Driven by Fractional Brownian Motion
Bin Pei, Yuzuru Inahama, Yong Xu
We focus on fast-slow systems involving both fractional Brownian motion (fBm) and standard Brownian motion (Bm). The integral with respect to Bm is the standard Ito integral, and t…
Stochastic flows and rough differential equations on foliated spaces
Yuzuru Inahama, Kiyotaka Suzaki
Stochastic differential equations (SDEs) on compact foliated spaces were introduced a few years ago. As a corollary, a leafwise Brownian motion on a compact foliated space was obta…
Asymptotic expansion of the density for hypoelliptic rough differential equation
Yuzuru Inahama, Nobuaki Naganuma
We study a rough differential equation driven by fractional Brownian motion with Hurst parameter . Under Hörmander's condition on the coefficient vector fields…
Paracontrolled quasi-geostrophic equation with space-time white noise
Yuzuru Inahama, Yoshihiro Sawano
We study the stochastic dissipative quasi-geostrophic equation with space-time white noise on the two-dimensional torus. This equation is highly singular and basically ill-posed in…
Heat trace asymptotics on equiregular sub-Riemannian manifolds
Yuzuru Inahama, Setsuo Taniguchi
We study a "div-grad type" sub-Laplacian with respect to a smooth measure and its associated heat semigroup on a compact equiregular sub-Riemannian manifold. We prove a short time…
Stochastic complex Ginzburg-Landau equation with space-time white noise
Masato Hoshino, Yuzuru Inahama, Nobuaki Naganuma
We study the stochastic cubic complex Ginzburg-Landau equation with complex-valued space-time white noise on the three dimensional torus. This nonlinear equation is so singular tha…
Short time full asymptotic expansion of hypoelliptic heat kernel at the cut locus
Yuzuru Inahama, Setsuo Taniguchi
In this paper we prove a short time asymptotic expansion of a hypoelliptic heat kernel on an Euclidean space and a compact manifold. We study the "cut locus" case, namely, the case…
Rough path theory and stochastic calculus
Yuzuru Inahama
T. Lyons' rough path theory is something like a deterministic version of K. Ito's theory of stochastic differential equations, combined with ideas from K. T. Chen's theory of itera…
Large deviations for rough path lifts of Watanabe's pullbacks of delta functions
Yuzuru Inahama
We study Donsker-Watanabe's delta functions associated with strongly hypoelliptic diffusion processes indexed by a small parameter. They are finite Borel measures on the Wiener spa…
Short time kernel asymptotics for rough differential equation driven by fractional Brownian motion
Yuzuru Inahama
We study a stochastic differential equation in the sense of rough path theory driven by fractional Brownian rough path with Hurst parameter H (1/3 < H <= 1/2) under the ellipticity…
Malliavin differentiability of solutions of rough differential equations
Yuzuru Inahama
In this paper we study rough differential equations driven by Gaussian rough paths from the viewpoint of Malliavin calculus. Under mild assumptions on coefficient vector fields and…