具有无限均值的超布朗运动的绝对连续性

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
R. Mamin, L. Mytnik
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引用次数: 3

摘要

在这项工作中,我们证明了对于任何维度$d\geq1$和(0,1)$超布朗运动中的任何$\gamma,对应于log拉普拉斯方程\bearth{equipment*}\beart{split}\frac{\partial v(t,x{R}_+\times\mathbb{R}^d,\\v(0,x)&=f(x)\end{split}\end{。我们的证明是基于\LL\方程解的性质。我们还证明了当初始数据$v(0,\cdot)$是一个有限的非零测度时,\LL\方程具有唯一的连续解。此外,该解决方案持续依赖于初始数据。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Absolute continuity of the super-Brownian motion with infinite mean
In this work we prove that for any dimension $d\geq 1$ and any $\gamma \in (0,1)$ super-Brownian motion corresponding to the log-Laplace equation \begin{equation*} \begin{split} \frac{\partial v(t,x)}{\partial t } & = \frac{1}{2}\bigtriangleup v(t,x) + v^\gamma (t,x) ,\: (t,x) \in \mathbb{R}_+\times \mathbb{R}^d,\\ v(0,x)&= f(x) \end{split} \end{equation*} is absolutely continuous with respect to the Lebesgue measure at any fixed time $t>0$. Our proof is based on properties of solutions of the \LL\ equation. We also prove that when initial datum $v(0,\cdot)$ is a finite, non-zero measure, then the \LL\ equation has a unique, continuous solution. Moreover this solution continuously depends on initial data.
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来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
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