研究者総覧

石川 保志 (イシカワ ヤスシ)

  • 大学院理工学研究科 数理物質科学専攻 准教授
Last Updated :2020/11/10

研究者情報

J-Global ID

研究キーワード

  • 確率論   数学   

研究分野

  • 自然科学一般 / 基礎解析学 / 確率論

所属学協会

  • アメリカ数学会   日本数学会   

研究活動情報

論文

  • Stochastic analysis on the Wiener-Poisson space and its application tothe nerve cell model
    Yasushi Ishikawa
    無限分解可能過程に関連する諸問題(24) 434 1 - 21 2020年03月 [招待有り]
     研究論文(大学,研究機関等紀要)
  • ISHIKAWA Yasushi, Hiroshi Kunita, Tsuchiya Masaaki
    Stochastic Processes and their Applications 128 9 3181 - 3219 2018年09月 [査読有り]
     研究論文(学術雑誌)
  • Yasushi Ishikawa, Takanobu Yamanobe
    Japan Journal of Industrial and Applied Mathematics 35 2 969 - 1004 2018年07月 [査読有り]
     研究論文(学術雑誌) 
    We introduce an asymptotic expansion of the transition density of a nonlinear oscillator involving a jump-diffusion process. We approximate the transition density by expanding the characteristic function of the solution to the nonlinear oscillator with respect to time and present a numerical verification of the asymptotic expansion of the transition density. This study provides us with a new mathematical framework for analyzing the dynamics of stochastic mathematical neuronal models using a jump–diffusion process.
  • Masafumi Hayashi, Yasushi Ishikawa
    MATHEMATISCHE NACHRICHTEN 285 5-6 619 - 658 2012年04月 [査読有り]
     研究論文(学術雑誌) 
    In this paper, we introduce the compositions of smooth Wiener-Poisson functional and Schwartz distribution by using Malliavin calculus jump type. We also prove Watanabe's theorem in the jump-diffusion case, that is, the asymptotic expansion formula for the compositions of a smooth Wiener-Poisson functional with Schwartz distributions.
  • Yasushi Ishikawa
    STOCHASTIC ANALYSIS WITH FINANCIAL APPLICATIONS, HONG KONG 2009 65 99 - 120 2011年 [査読有り][招待有り]
     研究論文(国際会議プロシーディングス) 
    In this paper we study an optimal stopping problem associated with jump-diffusion processes. We use a viscosity solution approach for the solution to HJB equality, which the value function should obey. Using the penalty method we obtain the existence of the value function as a viscosity solution to the HJB equation, and the uniqueness.
  • SIMON Thomas, 石川保志
    統計数理研究所共同研究リポート 213 104 - 132 2008年02月
  • Yasushi Ishikawa, Hiroshi Kunita
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS 116 12 1743 - 1769 2006年12月 [査読有り]
     研究論文(学術雑誌) 
    We study the existence and smoothness of densities of laws of solutions of a canonical stochastic differential equation (SDE) driven by a Levy process through the Malliavin calculus on the Wiener-Poisson space. Our assumption needed for the equation is very simple, since we are considering the canonical SDE. Assuming that the Levy process is nondegenerate, we prove the existence of a smooth density in the case where the coefficients of the equation are nondegenerate. Our main result is stated in Theorem 1.1. (c) 2006 Elsevier B.V. All rights reserved.
  • Y Ishikawa
    APPLIED MATHEMATICS AND OPTIMIZATION 50 1 21 - 65 2004年07月 [査読有り]
     研究論文(学術雑誌) 
    An optimal portfolio/control problem is considered for a two-dimensional model in finance. A pair consisting of the wealth process and cumulative consumption process driven by a geometric Levy process is controlled by adapted processes. The value function appears and turns out to be a viscosity solution to some integro-differential equation, by using the Bellman principle.
  • 石川 保志
    Progr. Probab. 53 129 - 149 2003年 [査読有り]
     研究論文(国際会議プロシーディングス) 
    In this paper we consider the asymptotic behaviour of the transition density for processes of jump type as the time parameter t tends to 0. We use Picard's duality method, which allows us to obtain the lower and upper bounds of the density even for the case where the support of Levy measure is singular. The main result is that, under certain restrictions, the density may exhibit an exponential type decrease as t --> 0 according to the accessibility of the objective points by a certain Markov chain.
  • Yasushi Ishikawa
    Tohoku Mathematical Journal 53 2 183 - 202 2001年06月 [査読有り]
     研究論文(学術雑誌) 
    We consider the asymptotic behaviour of the transition density for processes of jump type as the time parameter t tends to O. We use Picard's duality method, which allows us to obtain the lower and upper bounds of the density even for the case where the support of Lévy measure is singular. The main result is that, under certain restrictions, the density behaves in polynomial order or may decrease in exponential order as t → O according to geometrical conditions of the objective points.
  • Density estimate in small time for jump processes with singular Lévy measures and its support property
    石川 保志
    Funct. Differ. Equ. 8 3-4 273 - 285 2001年 [査読有り]
     研究論文(学術雑誌)
  • An example of non-local operators having no transmission property
    石川 保志
    Tsukuba J. Math. 25 1 399 - 411 2001年 [査読有り]
     研究論文(学術雑誌)
  • Yasushi Ishikawa
    Kyushu Journal of Mathematics 55 2 267 - 299 2001年 [査読有り]
     研究論文(学術雑誌)
  • Yasushi Ishikawa
    Proceedings of the Japan Academy Series A: Mathematical Sciences 77 6 79 - 83 2001年 [査読有り]
     研究論文(学術雑誌) 
    In this paper we consider the support property and the short time asymptotic behavior of the transition density for (possibly degenerate) processes of jump type whose Lévy measure is singular.
  • K Ichijo, Y Ishikawa, M Okada
    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 16 2 287 - 305 1999年06月 [査読有り]
     研究論文(学術雑誌) 
    The purpose of this note is to investigate the wavelet de-noising method in statistical inverse problems from real analysis point of view. Cases of deterministic and stochastic noises are discussed in a unified way.
  • Diagonal estimates of transition densities for jump processes in small time
    石川 保志, Remi Leandre
    Progr. Probab 42 251 - 273 1998年 [査読有り]
     研究論文(国際会議プロシーディングス)
  • Y Ishikawa
    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 33 2 179 - 222 1997年 [査読有り]
     研究論文(学術雑誌) 
    We give asymptotic upper and lower bounds of large deviation type for the transition density of a jump type processes on R(d), which is composed of stable-like processes on the line and vector fields on R(d). We use the theory of Malliavin calculus both for diffusion and for jump type processes. In the case where there is no drift, the upper and lower bounds coincide.
  • Yasushi Ishikawa
    Potential Analysis 6 1 11 - 37 1997年 [査読有り]
     研究論文(学術雑誌) 
    We present a point-wise concrete upper bounds in a small time for transition densities of truncated stable processes in Rd, which have singular Lévy measures. We provide several examples.
  • Yasushi Ishikawa
    Tohoku Mathematical Journal 46 443 - 456 1994年01月 [査読有り]
     
    The Markov process of pure jump type given by S.D.E. has a smooth density under non-degeneracy conditions both on the coefficient and on the Lévy measure of the driving Lévy process. In this case we obtain an estimate of this density when the time parameter is small. In this way we extend the Léandre estimate of the density for pure jump processes. © 1994 Tohoku University, Mathematical Institute.
  • Yasushi Ishikawa
    Tohoku Mathematical Journal 46 4 443 - 456 1994年 [査読有り]
     研究論文(学術雑誌) 
    The Markov process of pure jump type given by S.D.E. has a smooth density under non-degeneracy conditions both on the coefficient and on the Lévy measure of the driving Lévy process. In this case we obtain an estimate of this density when the time parameter is small. In this way we extend the Léandre estimate of the density for pure jump processes. © 1994 Tohoku University, Mathematical Institute.
  • Y ISHIKAWA
    BULLETIN DES SCIENCES MATHEMATIQUES 117 4 463 - 483 1993年 [査読有り]
     研究論文(学術雑誌) 
    A pure jump type stochastic process on R(d) driven by one-dimensional Levy processes of pure jump type and the vector fields is considered. If the vector fields are non-degenerate then the semigroup associated to the process has a smooth density p(t) (x, y). Our result is the following: If the minimum of the ''weights'' of the polygonal paths connecting x is-an-element-of R(d) to y is-an-element-of R(d)(y not-equal x) is kappa then lim inf(t-->0)(1/t(kappa))p(t)(x, y) greater-than-or-equal-to C. Further we can give an expression of the constant C in terms of ''polygonal expression'' of the big jump trajectories.
  • Y ISHIKAWA
    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN 42 1 171 - 184 1990年01月 [査読有り]
     研究論文(学術雑誌)
  • 石川 保志
    Tokyo J. Math 12 1 131 - 143 1989年 [査読有り]
     研究論文(学術雑誌)
  • Remarks on transmission, antitransmission and antilocal properties for sums of stable generators
    石川 保志
    Tsukuba J. Math. 12 2 477 - 487 1988年 [査読有り]
     研究論文(学術雑誌)
  • antilocality and one-sided antilocality for stable generators on the line
    石川 保志
    Tsukuba J. Math 10 1 1 - 9 1986年 [査読有り]
     研究論文(学術雑誌)

書籍

講演・口頭発表等

  • Analysis of jumps processes and their applications  [招待講演]
    石川 保志
    無限分解可能過程に関連する諸問題 2019年11月
  • Stochastic analysis on the Wiener-Poisson space and its application to the nerve cell model  [招待講演]
    石川 保志
    Workshop on Stochastic Analysis and Applications 2019年06月
  • Smooth density and its short time estimate for jump process determined by SDE  [通常講演]
    石川 保志
    Workshop in Stochastic Analysis and Applications 2018年08月 口頭発表(一般)
  • 年金と保険の基礎  [通常講演]
    石川 保志
    愛媛大学公開講座(理学部) 2015年11月
  • あなたの身近な年金と保険  [通常講演]
    石川 保志
    愛媛大学オープンキャンパス 2015年08月
  • Analysis on the Wiener-Poisson space and its application to Ito type SDE  [通常講演]
    石川 保志
    3rd Austrian stochastic days 2014年09月 口頭発表(招待・特別)
  • 生保の仕組み  [通常講演]
    石川 保志
    教員免許更新講習 2012年08月
  • 保険の仕組み  [通常講演]
    石川 保志
    教員免許更新講習 2009年08月

MISC

受賞

  • 2011年02月 Elsevier Most Cited Articles in 2006-2010 (Stochastic Processes and their Applications)
     
    受賞者: 石川 保志;国田 寛

委員歴

  • 2017年04月 - 2018年03月   愛媛大学遺伝子組み換え実験施設委員
  • 2016年02月 - 2016年02月   採点委員

愛媛大学教員活動実績

教育活動(B)

担当授業科目(B01)

  • 2019, 前期, 学部, 確率統計Ⅰ
  • 2019, 前期, 学部, 確率統計続論
  • 2019, 前期, 学部, 卒業研究Ⅰ
  • 2019, 前期, 修士, 実解析学
  • 2019, 前期, 修士, 数理科学ゼミナールⅠ
  • 2019, 前期, 修士, 数理科学ゼミナールⅢ


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