Infinite-dimensional stochastic differential equations and tail σ-fields II: the IFC condition

Yosuke Kawamoto, Hirofumi Osada, Hideki Tanemura

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)79-128
Number of pages50
JournalJournal of the Mathematical Society of Japan
Volume74
Issue number1
DOIs
Publication statusPublished - 2022

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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