Green Function Estimates and Harnack Inequality for Subordinate Brownian Motions
Green Function Estimates and Harnack Inequality for Subordinate Brownian Motions
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从属布朗运动的格林函数估计和 Harnack 不等式
DOI：
10.1007/s11118-005-9003-z
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发表时间：
2006
影响因子：
1.1
通讯作者：
Z. Vondraček
中科院分区：
文献类型：
--
作者：
M. Rao;R. Song;Z. Vondraček
设X是%MathType！Translator！2！1！AMS LaTeX.tdl！tex--am-LaTeX！%MathType！MTEF！2！1！+-%feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX%garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz%aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq%Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq%Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaacq%WIDesOdaahaaWcbeqaaiaadsgaaaaaaa！3A16！$$\mathbb{R}^{d}$$中的L进程，%MathType！Translator！2！1！AMS LaTeX.tdl！TeX--AMS-LaTeX！%MathType！MTEF！2！1！+-%feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX%garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz%aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq%Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq%Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaaca%WGKbGaeyyzImRaaG4maaaa！3AFC！$$d\geqslant 3$$，通过从属具有正漂移的布朗运动而获得。这一过程与独立的布朗运动和不含连续分量的L过程之和具有相同的规律。研究了X的格林函数在零点附近的渐近行为。在从属函数的拉普拉斯指数是完全Bernstein函数的假设下，我们还刻画了格林函数在无穷远处的渐近行为。通过对从属函数的L测度的一个附加假设，证明了Harnack不等式对X的非负调和函数是成立的。
Let X be a Lévy process in% MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!% MathType!MTEF!2!1!+-% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaacq% WIDesOdaahaaWcbeqaaiaadsgaaaaaaa!3A16!$$\mathbb{R}^{d} $$, % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX!% MathType!MTEF!2!1!+-% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaaca% WGKbGaeyyzImRaaG4maaaa!3AFC!$$d \geqslant 3$$, obtained by subordinating Brownian motion with a subordinator with a positive drift. Such a process has the same law as the sum of an independent Brownian motion and a Lévy process with no continuous component. We study the asymptotic behavior of the Green function of X near zero. Under the assumption that the Laplace exponent of the subordinator is a complete Bernstein function we also describe the asymptotic behavior of the Green function at infinity. With an additional assumption on the Lévy measure of the subordinator we prove that the Harnack inequality is valid for the nonnegative harmonic functions of X.