On linear stochastic flows

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2023-11-08 DOI:10.1090/tran/8782

Beniamin Goldys, Szymon Peszat

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引用次数: 0

Abstract

We study the existence of the stochastic flow associated to a linear stochastic evolution equation d ⁡ X = A X d ⁡ t + ∑ k B k X d ⁡ W k , \begin{equation*} \operatorname {d} X= AX\operatorname {d} t +\sum _{k} B_k X\operatorname {d} W_k, \end{equation*} on a Hilbert space. Our first result covers the case where A A is the generator of a C 0 C_0 -semigroup, and ( B k ) (B_k) is a sequence of bounded linear operators such that ∑ k ‖ B k ‖ > + ∞ \sum _k\|B_k\|>+\infty . We also provide sufficient conditions for the existence of stochastic flows in the Schatten classes beyond the space of Hilbert–Schmidt operators. Some new results and examples concerning the so-called commutative case are presented as well.

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关于线性随机流

研究了Hilbert空间上线性随机演化方程d (X) = a (X) d (t) +∑k (B) k (X) d (W) k, \begin{equation*} \operatorname {d} X= AX\operatorname {d} t +\sum _{k} B_k X\operatorname {d} W_k, \end{equation*}的存在性。我们的第一个结果涵盖了A A是C 0 C＿0 -半群的生成器，并且(B k) (B＿k)是一个有界线性算子序列，使得∑k‖B k‖＆gt;+∞\sum ＿k\|B＿k\|＆gt;+ \infty。我们还提供了在Hilbert-Schmidt算子空间之外的Schatten类中随机流存在的充分条件。文中还给出了一些关于交换情况的新结果和例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.