具有跳变噪声驱动的螺旋的随机朗道-利夫希茨-吉尔伯特方程的良好拟合

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2024-10-15 DOI:10.1016/j.spl.2024.110285

Soham Gokhale

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引用次数: 0

摘要

我们考虑由纯跳跃噪声驱动的随机兰道-利夫希茨-吉尔伯特方程。我们假设螺旋项对总能量的贡献为非零。利用有限维近似和非度量空间的 Jakubowski 版 Skorohod 定理的广义，我们证明了所考虑的问题有一个弱马丁格尔解。将问题限制在维数 1，我们证明了所得到的解在路径上是唯一的，从而得出了强解存在的结论。

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Well-posedness for the stochastic Landau–Lifshitz–Gilbert equation with helicity driven by jump noise

We consider the stochastic Landau–Lifshitz–Gilbert equation driven by pure jump noise. We assume non-zero contribution from the helicity term to the total energy. Using finite dimensional approximation followed by a generalization of the Jakubowski’s version of the Skorohod Theorem for non-metric spaces, we show that the considered problem admits a weak martingale solution. Restricting the problem to dimension 1, we show that the obtained solution is pathwise unique, thereby concluding the existence of a strong solution.

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

期刊介绍： Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature. Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission. The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability. The mainstream of Letters will focus on new statistical methods, theoretical results, and innovative applications of statistics and probability to other scientific disciplines. Key results and central ideas must be presented in a clear and concise manner. These results may be part of a larger study that the author will submit at a later time as a full length paper to SPL or to another journal. Theory and methodology may be published with proofs omitted, or only sketched, but only if sufficient support material is provided so that the findings can be verified. Empirical and computational results that are of significant value will be published.