Infinite-dimensional stochastic differential equations and tail $\sigma$-fields II: the IFC condition
-
- Kawamoto Yosuke
- Fukuoka Dental College
-
- Osada Hirofumi
- Faculty of Mathematics, Kyushu University
-
- Tanemura Hideki
- Department of Mathematics, Keio University
書誌事項
- タイトル別名
-
- Infinite-dimensional stochastic differential equations and tail 𝜎-fields II: the IFC condition
この論文をさがす
抄録
<p>In a previous report, the second and third authors gave general theorems for unique strong solutions of infinite-dimensional stochastic differential equations (ISDEs) describing the dynamics of infinitely many interacting Brownian particles. One of the critical assumptions is the “IFC” condition. The IFC condition requires that, for a given weak solution, the scheme consisting of the finite-dimensional stochastic differential equations (SDEs) related to the ISDEs exists. Furthermore, the IFC condition implies that each finite-dimensional SDE has unique strong solutions. Unlike other assumptions, the IFC condition is challenging to verify, and so the previous report only verified it for solutions given by quasi-regular Dirichlet forms. In the present paper, we provide a sufficient condition for the IFC requirement in more general situations. In particular, we prove the IFC condition without assuming the quasi-regularity or symmetry of the associated Dirichlet forms. As an application of the theoretical formulation, the results derived in this paper are used to prove the uniqueness of Dirichlet forms and the dynamical universality of random matrices.</p>
収録刊行物
-
- Journal of the Mathematical Society of Japan
-
Journal of the Mathematical Society of Japan 74 (1), 79-128, 2022
一般社団法人 日本数学会
- Tweet
キーワード
詳細情報 詳細情報について
-
- CRID
- 1390572321594249600
-
- NII論文ID
- 130008144193
-
- NII書誌ID
- AA0070177X
-
- ISSN
- 18811167
- 18812333
- 00255645
-
- NDL書誌ID
- 031943451
-
- 本文言語コード
- en
-
- データソース種別
-
- JaLC
- NDL
- Crossref
- CiNii Articles
- KAKEN
-
- 抄録ライセンスフラグ
- 使用不可