AIDA, Shigeki

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Title
Professor
Field
Probability theory
Research interests
Infinite dimensional analysis, Malliavin calculus, Rough paths, Stochastic analysis on loop spaces, Stochastic differential equations
Current research

I am interested in infinite dimensional analysis arsing from the study of problems in probability theory. For example, I am studying the semi-classical limit of infinite dimensional Schrödinger operators, asymptotic behaviour of the spectral gap on loop spaces, stochastic differential equations, rough differential equations.

Selected publications
  1. S.Aida, S.Kusuoka and D.W.Stroock,On the Support of Wiener Functionals, Asymptotic Problems in Probability Theory:Wiener functonals and asymptotics (Sanda/Kyoto, 1990), 3--34,Pitman Res. Notes Math. Ser., 284, Longman Sci. Tech., Harlow, 1993.
  2. S.Aida, T.Masuda and I.Shigekawa,Logarithmic Sobolev inequalities and exponential integrability, J. Funct. Anal. 126 (1994), no.1,83--101
  3. S.Aida,Uniform positivity improving property, Sobolev inequality and spectral gaps, J.Funct.Anal.,158 (1998) no.1, 152--185.
  4. S.Aida,Weak Poincare inequalities on domains defined by Brownian rough paths,Ann. Probab., 32 (2004) no.4, 3116--3137.
  5. S.Aida,Tunneling for spatially cut-off P(φ)_2-Hamiltonians, J.Funct.Anal. Vol 263 no.9 (2012), 2689--2753.
  6. S.Aida and K.Sasaki,Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces, Stochastic Process. Appl. 123 (2013), no.10, 3800--3827.
  7. S.Aida,Reflected rough differential equations, Stochastic Process. Appl., 125, (2015), no.9, 3570-3595.
  8. S.Aida,Asymptotics of spectral gaps on loop spaces over a class of Riemannian manifolds,J. Funct.Anal., 269 (2015), no.12, 3714-3764.

Memberships, activities and

Awards

The Mathematical Society of Japan

The MSJ Analysis Prize 2007