论文标题
加热内核界限，用于大型马尔可夫过程，并具有单一的跳跃
Heat kernel bounds for a large class of Markov process with singular jump
论文作者
论文摘要
令$ z =（z^{1}，\ ldots，z^{d}）$为$ d $ -dimensionallévy流程，其中$ z^{i} $是独立的$ 1 $ - 二级lévyvy流程，带有跳跃kernel $ j^{ϕ，1}（u，w）（u，w）（u，w） = | u-w |^{ - 1} ϕ（| u-w |）^{ - 1} $ for $ u，w \ in \ mathbb r $。这里$ ϕ $是一个增加的功能，具有较弱的缩放条件$ \ $ \下列α，\overlineα\ in（0，2）$。 令$ j（x，y）\ asymp j^ϕ（x，y）$为对称的可测量函数，其中\ begin \ begin {align*} j^ϕ（x，y）：= \ begin {case} j^{st j^{st j {case}，1}，1}（x^i，y^i，y，y^i）所有$ j \ ne i $} \\ 0 \ qquad＆\ text {如果$ x^i \ ne y^i $的y^j $多于一个索引$ i $。} \ end {cases} \ end {cases} \ end {align {align {align*}对应于跳跃内核$ j $的存在\ ldots，x^{d}）$，并获得过渡密度函数的尖锐的两侧热核估计。
Let $Z=(Z^{1}, \ldots, Z^{d})$ be the $d$-dimensional Lévy processes where $Z^{i}$'s are independent $1$-dimensional Lévy processes with jump kernel $J^{ϕ, 1}(u,w) =|u-w|^{-1}ϕ(|u-w|)^{-1}$ for $u, w\in \mathbb R$. Here $ϕ$ is an increasing function with weak scaling condition of order $\underline α, \overline α\in (0, 2)$. Let $J(x,y) \asymp J^ϕ(x,y)$ be the symmetric measurable function where \begin{align*} J^ϕ(x,y):=\begin{cases} J^{ϕ, 1}(x^i, y^i)\qquad&\text{ if $x^i \ne y^i$ for some $i$ and $x^j = y^j$ for all $j \ne i$}\\ 0\qquad&\text{ if $x^i \ne y^i$ for more than one index $i$.} \end{cases} \end{align*} Corresponding to the jump kernel $J$, we show the existence of non-isotropic Markov processes $X:=(X^{1}, \ldots, X^{d})$ and obtain sharp two-sided heat kernel estimates for the transition density functions.
