Study on occupation times of fractional Brownian motion

• Project/Area Number: 25400128
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Chuo University
• Principal Investigator: Kosugi Nobuko 中央大学, 経済学部, 教授 (20302995)
• Project Period (FY): 2013-04-01 – 2019-03-31
• Project Status: Completed (Fiscal Year 2018)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 共分散行列 / フラクショナル・ブラウン運動 / 多項式行列

Outline of Final Research Achievements

Fractional Brownian motion is a self-similar Gaussian process, and hence its distribution is determined by expectation and variance.
To study on occupation times of n-dimensional fractional Brownian motion, we need to consider the asymptotic behavior of its covariance matrix.
Thus, we showed an evaluation of determinant of covariance matrix of n-dimensional fractional Brownian motion with Hurst parameter H (1/2<H<1).

Academic Significance and Societal Importance of the Research Achievements

フラクショナル・ブラウン運動の自己相似性の指数 H は 0＜H＜1 の範囲で定義されているが、これまでの滞在時間に関する研究においては、指数を 0＜H≦1/2 に限定したものが多かった。これは、1/2＜H＜1の場合に、フラクショナル・ブラウン運動の共分散行列の行列式を下から評価することが難しいことによる。そこで本研究では、1/2＜H＜1 の場合に、共分散行列の行列式がある意味において下から評価できることを示した。

Research Products

• [Journal Article] A note on the correlation matrix of fractional Brownian motion (2019)
  • Author(s): Nobuko Kosugi
  • Journal Title: International Mathematical Forum Volume: 14 Issue: 2 Pages: 69-72
  • DOI: 10.12988/imf.2019.917
  • Peer Reviewed / Open Access
• [Journal Article] A new approach to Bezout equations derived from multivariate polynomial matrices and real entire functions (2015)
  • Author(s): Koichi Suyama and Nobuko Kosugi
  • Journal Title: Linear and Multilinear Algebra Volume: 63 Issue: 11 Pages: 2318-2331
  • DOI: 10.1080/03081087.2015.1008969
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Bezout equations over bivariate polynomial matrices related by an entire function (2015)
  • Author(s): Koichi Suyama and Nobuko Kosugi
  • Journal Title: Linear and Multilinear Algebra Volume: 63 Issue: 6 Pages: 1138-1153
  • DOI: 10.1080/03081087.2014.922968
  • Peer Reviewed
• [Journal Article] Bezout equations over bivariate polynomial matrices related by an entire function (2014)
  • Author(s): Koichi Suyama and Nobuko Kosugi
  • Journal Title: Linear and Multilinear Algebra
  • Peer Reviewed
• [Journal Article] Digital redesign of infinite-dimensional controllers based on numerical integration of new representation (2013)
  • Author(s): Nobuko Kosugi and Koichi Suyama
  • Journal Title: Systems & Control Letters Volume: 62 Issue: 7 Pages: 531-538
  • DOI: 10.1016/j.sysconle.2013.03.007
  • Peer Reviewed