| SHIOZAWA Yuichi |  |
| Faculty of Science and Engineering Department of Mathematical Sciences | |
| Professor |
Last Updated :2025/05/31
Researcher Profile and Settings
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Research Areas
Research Experience
- 同志社大学, 理工学部数理システム学科, 教授, 2024/04 - Today
- Osaka University, 大学院理学研究科数学専攻, 准教授, 2017/03 - 2024/03
- Okayama University, The Graduate School of Natural Science and Technology, 准教授, 2009/04 - 2017/02
- Kyoto University, Graduate School of Science Division of Mathematics, GCOE 特定助教, 2008/10 - 2009/03
- Ritsumeikan University, College of Science and Engineering, 数学嘱託講師, 2007/04 - 2008/09
Published Papers
- Berry-Esseen bound for the Brownian motions on hyperbolic spaces
Yuichi Shiozawa
Studia Mathematica, 277(3) 213 - 241, Sep. 2024, Scientific journal - Hausdorff dimensions of inverse images and collision time sets for symmetric Markov processes
Yuichi Shiozawa; Jian Wang
Electronic Journal of Probability, Institute of Mathematical Statistics, 29, 15 Jan. 2024, Scientific journal - Transience of symmetric nonlocal Dirichlet forms
Yuichi Shiozawa
Mathematische Nachrichten, Wiley, 296(5) 2121 - 2149, 08 Feb. 2023, Scientific journal - Compactness of Semigroups Generated by Symmetric Non-Local Dirichlet Forms with Unbounded Coefficients
Yuichi Shiozawa; Jian Wang
Potential Analysis, Springer Science and Business Media LLC, 58(2) 373 - 392, Feb. 2023, Scientific journal - Limiting behaviors of generalized elephant random walks
Yuichi Shiozawa
Journal of Mathematical Physics, AIP Publishing, 63(12) 123504 - 123504, 01 Dec. 2022, Scientific journal - Maximal Displacement of Branching Symmetric Stable Processes
Yuichi Shiozawa
Springer Proceedings in Mathematics and Statistics, 394 461 - 491, 2022, International conference proceedings - Limiting distributions for the maximal displacement of branching Brownian motions
Yasuhito Nishimori; Yuichi Shiozawa
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, MATH SOC JAPAN, 74(1) 177 - 216, Jan. 2022, Scientific journal - Martingale Nature and Laws of the Iterated Logarithm for Markov Processes of Pure-Jump Type
Yuichi Shiozawa; Jian Wang
JOURNAL OF THEORETICAL PROBABILITY, SPRINGER/PLENUM PUBLISHERS, 34(4) 2005 - 2032, Dec. 2021, Scientific journal - Maximal displacement and population growth for branching brownian motions
Yuichi Shiozawa
Illinois Journal of Mathematics, 63(3) 353 - 402, Oct. 2019, Scientific journal - Long-time heat kernel estimates and upper rate functions of Brownian motion type for symmetric jump processes
Yuichi Shiozawa; Jian Wang
Bernoulli, 25(4 B) 3796 - 3831, 2019, Scientific journal - Bottom crossing probability for symmetric jump processes
Yuichi Shiozawa
MATHEMATISCHE ZEITSCHRIFT, SPRINGER HEIDELBERG, 287(3-4) 1355 - 1376, Dec. 2017, Scientific journal - Escape rate of the Brownian motions on hyperbolic spaces
Yuichi Shiozawa
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, JAPAN ACAD, 93(4) 27 - 29, Apr. 2017, Scientific journal - Rate Functions for Symmetric Markov Processes via Heat Kernel
Yuichi Shiozawa; Jian Wang
POTENTIAL ANALYSIS, SPRINGER, 46(1) 23 - 53, Jan. 2017, Scientific journal - ESCAPE RATE OF SYMMETRIC JUMP-DIFFUSION PROCESSES
Yuichi Shiozawa
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, AMER MATHEMATICAL SOC, 368(11) 7645 - 7680, Nov. 2016, Scientific journal - Lower Escape Rate of Symmetric Jump-diffusion Processes
Yuichi Shiozawa
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, CANADIAN MATHEMATICAL SOC, 68(1) 129 - 149, Feb. 2016, Scientific journal - A remark on the uniqueness of Silverstein extensions of symmetric Dirichlet forms
Kazuhiro Kuwae; Yuichi Shiozawa
MATHEMATISCHE NACHRICHTEN, WILEY-V C H VERLAG GMBH, 288(4) 389 - 401, Mar. 2015, Scientific journal - Conservation property of symmetric jump-diffusion processes
Yuichi Shiozawa
FORUM MATHEMATICUM, WALTER DE GRUYTER GMBH, 27(1) 519 - 548, Jan. 2015, Scientific journal - Explosion of Jump-Type Symmetric Dirichlet Forms on R-d
Yuichi Shiozawa; Toshihiro Uemura
JOURNAL OF THEORETICAL PROBABILITY, SPRINGER/PLENUM PUBLISHERS, 27(2) 404 - 432, Jun. 2014, Scientific journal - Upper escape rate of Markov chains on weighted graphs
Xueping Huang; Yuichi Shiozawa
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, ELSEVIER SCIENCE BV, 124(1) 317 - 347, Jan. 2014, Scientific journal - LOCALIZATION FOR BRANCHING BROWNIAN MOTIONS IN RANDOM ENVIRONMENT
Yuchi Shiozawa
TOHOKU MATHEMATICAL JOURNAL, TOHOKU UNIVERSITY, 61(4) 483 - 497, Dec. 2009, Scientific journal - Central Limit Theorem for Branching Brownian Motions in Random Environment
Yuichi Shiozawa
JOURNAL OF STATISTICAL PHYSICS, SPRINGER, 136(1) 145 - 163, Jul. 2009, Scientific journal - Exponential growth of the numbers of particles for branching symmetric alpha-stable processes
Yuichi Shiozawa
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, MATH SOC JAPAN, 60(1) 75 - 116, Jan. 2008, Scientific journal - Limit theorems for branching Markov processes
Zhen-Qing Chen; Yuichi Shiozawa
JOURNAL OF FUNCTIONAL ANALYSIS, ACADEMIC PRESS INC ELSEVIER SCIENCE, 250(2) 374 - 399, Sep. 2007, Scientific journal - Extinction of branching symmetric alpha-stable processes
Yuichi Shiozawa
JOURNAL OF APPLIED PROBABILITY, APPLIED PROBABILITY TRUST, 43(4) 1077 - 1090, Dec. 2006, Scientific journal - Variational formula for Dirichlet forms and estimates of principal eigenvalues for symmetric alpha-stable processes
Y Shiozawa; M Takeda
POTENTIAL ANALYSIS, SPRINGER, 23(2) 135 - 151, Sep. 2005, Scientific journal - Principal eigenvalues for time changed processes of one-dimensional α-stable processes
Yuichi Shiozawa
Probability and Mathematical Statistics, 24(2) 355 - 366, 2004
MISC
- Escape rate of symmetric Markov processes (Symposium on Probability Theory)
塩沢 裕一
数理解析研究所講究録, 京都大学数理解析研究所, 1903 165 - 167, Jul. 2014 - Branching Brownian motions in random environment (Stochastic Analysis of Jump Processes and Related Topics)
Shiozawa Yuichi
RIMS Kokyuroku, Kyoto University, 1672 143 - 158, Jan. 2010
Research Projects
- Symmetric Markov processes: sample path analysis and functional analytic properties
塩沢 裕一; 森 隆大; 松浦 浩平
１）代表者 塩沢は、Jian Wang 氏（Fujian Normal University）との共同研究で、対称マルコフ過程が与えられた集合に滞在する時刻全体、および測度距離空間上の２つの独立な対称マルコフ過程が与えられた集合で衝突する時刻全体のハウスドルフ次元を決定した。今回の研究成果は、熱核評価を通じた解析に基づき、測度距離空間上のマルコフ過程、特にフラクタル上のブラウン運動や対称安定型過程にも適用可能である。本研究成果を国際研究集会などで発表するとともに、確率論の専門誌で論文として公表した。 ２）代表者 塩沢は、Jian Wang 氏（Fujian Normal University）との共同研究で、レビ型雑音を持つ分数べき確率熱方程式に対して、解の空間方向に対する大域的性質を調べた。確率熱方程式の主要部が分数べきラプラス作用素になることで、裾の重さが解の存在性および大域的性質に影響を与えることが明確になった。 ３）分担者 松浦は、京都大学の日野正訓氏とその学生であった真木新太氏との共同研究において、領域上の反射壁ブラウン運動に対する離散近似を得、結果に関する論文の執筆と投稿を行なった。この近似は領域の分割上のマルコフ連鎖によるもので、不均一な分割を例に含む。また、京都産業大学の森隆大氏との共同研究において、マルコフ過程のフェラー性について議論し、ポテンシャル論的な必要十分条件について既存の結果を整理した。 ４）分担者 森はディリクレ形式の境界理論の観点からキャパシティーを特徴付ける研究を行った。また、指数 $p>2$ のルベーグ空間へのディリクレ空間のコンパクト埋め込みについて研究を行い、熱核の文脈での同値条件を得た。 ５）研究集会「マルコフ過程とその周辺」では、本研究費で講演者の旅費援助を行った。また、研究集会やセミナーで研究成果を報告し、情報収集を行った。, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, 2023/04 -2028/03, Grant-in-Aid for Scientific Research (B) - マルコフ過程の線形増大に関する現象の普遍性
塩沢 裕一
前年度に引き続いて、双曲空間上のブラウン運動に対する Berry-Esseen 型定理の研究に取り組んだ。前年度末の時点では、空間次元が 3 のときに限って Berry-Esseen 型定理を得ていた。本年度は、空間次元が一般の場合に Berry-Esseen 型定理を得ることができた。特に、収束レートは通常の Berry-Esseen 型定理と変わらないことが分かった。さらに、空間次元が 2 もしくは奇数のときには、今回得た収束の速さが精密であることも示した。
前年度末の時点では、一般の空間次元の場合を扱うために、Gruet (1996) による、推移確率の積分表示を積極的に取り入れる方針に変更した。本年度は実際に、この方針に沿って計算を実行することを試みた。しかし、先に述べた積分表示の解析が難しく、計算を進めることができなかった。そこで方針を変更し、Millson の公式と呼ばれる、異なる次元に対応する推移確率たちに関する再帰式を用いることにした。すると、この公式と部分積分の公式とを繰り返し適用することで、分布に関する計算を実行することが可能となり、Berry-Esseen 型定理を証明するに至った。
この研究成果を論文にまとめて投稿した。さらに、本成果について研究集会「Dirichlet Forms and Related Topics」および「確率解析とその周辺」で発表するとともに、結果の一般化の可能性などについて参加者と議論した。, 日本学術振興会, 科学研究費助成事業, 2022/06 -2025/03, 挑戦的研究(萌芽), 大阪大学 - Analysis of global properties of symmetric Markov processes
Shiozawa Yuichi
In this research project, we characterized the global properties of a jump-type symmetric Markov process and the functional analytic properties of a Markov semigroup in terms of the spatial dimension, and of the coefficients and jumping kernel of the associated Dirichlet form. We further provided a sufficient condition for the LIL-type asymptotic properties of a non-symmetric jump process in terms of the existence of the second moment of the jumping kernel. We also revealed the global properties and the asymptotic properties of the tail distribution for the maximal displacement of a branching Brownian motion., Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, 2017/04 -2021/03, Grant-in-Aid for Scientific Research (C), Osaka University - Sample path analysis for symmetric Markov processes and Dirichlet forms
Shiozawa Yuichi
We developed the sample path analysis for symmetric Markov processes generated by regular Dirichlet forms. We first gave estimates on the speed of particles escaping to infinity (lower escape rate) under the condition on the volume growth or heat kernel. We further proved that some integral in the estimates above expresses the decay rate of some tail probability related to the lower escape rate. We next determined the escape rate of the Brownian motions on hyperbolic spaces. We finally proved that for branching Brownian motions on the Euclidean space, the spread rate is determined by the principal eigenvalue of some Schro"dinger type operator under some suitable condition., Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), 2014/04 -2017/03, Grant-in-Aid for Scientific Research (C), Okayama University - Analysis of asymptotic behaviors of Markov processes
SHIOZAWA Yuichi
Conservativeness criteria and upper estimates of the escape rate are established for symmetric jump-diffusion processes generated by regular Dirichlet forms. Furthermore, these results are proved to be sharp by using concrete examples. It is also prove that the Silverstein extension of a regular Dirichlet form is unique under some topological property of the associated intrinsic metric., Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B), 2011 -2013, Grant-in-Aid for Young Scientists (B), Okayama University - Analysis of asymptotic properties of branching Markov processes
SHIOZAWA Yuuichi
I studied about branching Brownian motions in random environment. As a result, it is proved that, even if the process may go extinct, the localization in weak sense occurs under the survival event. I also studied about symmetric Markov processes of pure jump-type and gave a sufficient condition for them to be conservative. I then constructed the explosive process of pure jump-type by the time change of symmetric stable process, which verifies that our sufficient condition is sharp., Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B), 2009 -2010, Grant-in-Aid for Young Scientists (B), Okayama University