Seiichiro Kusuoka

An inverse problem for stochastic differential equations

We discuss the problem of reconstructing the drift coefficient of a diffusion from the knowledge of the transition probabilities outside a given bounded region in ℝd,d>1. We also give an interpretation of the solution of this inverse problem in the framework of stochastic mechanics.

Predictability of wintertime stratospheric circulation examined using a nonstationary fluctuation-dissipation relation

AbstractThe dynamics and predictability of stratospheric low-frequency variability in the Northern Hemisphere winter are examined using a two-dimensional (2D) phase space spanned by the leading empirical orthogonal functions of the 10-hPa geopotential height field. The 2D phase space represents the variation of the strength of the polar night jet and the amplitude of zonal wavenumber-1 eddy components. A linearized nonstationary fluctuation–dissipation relation (NFDR) is developed based on the deterministic drift vector and the stochastic diffusion tensor estimated from a reanalysis dataset. The authors find that the solution of the linearized NFDR with an optimal data sampling time interval for estimating the drift vector and the diffusion tensor provides a good representation in the phase space of the inhomogeneous distribution of the forecast spread of the operational ensemble forecast conducted by the Japan Meteorological Agency. In particular, the linearized NFDR captures the local maximum of the for...

On smoothing properties of transition semigroups associated to a class of SDEs with jumps

We prove smoothing properties of nonlocal transition semigroups associated to a class of stochastic differential equations (SDE) in

Characterization of the convergence in total variation and extension of the Fourth Moment Theorem to invariant measures of diffusions

\mathbb{R} ^{d}

Exponential convergence of Markovian semigroups and their spectra on L p -spaces

driven by additive pure-jump Levy noise. In particular, we assume that the Levy process driving the SDE is the sum of a subordinated Wiener process

Diffusion processes in thin tubes and their limits on graphs

Y

Recurrence of the Brownian Motion in Multidimensional Semi-selfsimilar Environments and Gaussian Environments

(i.e.

Hölder and Lipschitz continuity of the solutions to parabolic equations of the non-divergence type

Y=W\circ T

Stein’s method for invariant measures of diffusions via Malliavin calculus☆

, where

Malliavin calculus for stochastic differential equations driven by subordinated Brownian motions

T