论文标题
迭代的对数法律，用于马尔可夫流程的职业时间
Laws of the iterated logarithm for occupation times of Markov processes
论文作者
论文摘要
在本文中，我们讨论了迭代对数（LIL）在马尔可夫流程的占用时间$ y $中的一般度量测量空间$ y $的法律，无论是在某些最小的假设下，均接近零和无穷大附近。我们首先在Balls $ b（x，r）radii $ r $的球上建立（截断）职业时间的lils lils $ $ $ $ $φ（r）$，这是$ y $的平均出口时间的迭代对数，通过显示功能$φ$是最佳的。我们对职业时间的最终结果涵盖了无穷大的零和接近无穷大的结果。我们的假设确实在零时是本地的，在我们截断的职业时间中的功能$φ$ $ r \ mapsto \ int_0^{φ（x，x，r）} {\ bf 1} _ {b（x，x，r）}（y__s）（y_s）ds $都取决于太空可变$ x $。我们还证明，总职业时间的类似LIL $ r \ mapsto \ int_0^\ infty {\ bf 1} _ {b（x，r）}（y__s）ds $在过程是瞬态时保持。然后，我们建立了有关职业时间的大时间行为$ t \ mapsto \ int_0^t {\ bf 1} _ {a}（y_s）ds $ 在保证过程复发的额外条件下。我们的结果涵盖了大量的砍伐者（征收）过程，具有远距离跳跃的随机电导模型，具有混合多项式局部生长的跳跃过程以及带有单数跳跃内核的跳跃过程。
In this paper, we discuss the laws of the iterated logarithm (LIL) for occupation times of Markov processes $Y$ in general metric measure space both near zero and near infinity under some minimal assumptions. We first establish LILs of (truncated) occupation times on balls $B(x,r)$ of radii $r$ up to an function $Φ(r)$, which is an iterated logarithm of mean exit time of $Y$, by showing that the function $Φ$ is optimal. Our first result on LILs of occupation times covers both near zero and near infinity regardless of transience and recurrence of the process. Our assumptions are truly local in particular at zero and the function $Φ$ in our truncated occupation times $r \mapsto\int_0^{ Φ(x,r)} {\bf 1}_{B(x,r)}(Y_s)ds$ depends on space variable $x$ too. We also prove that a similar LIL for total occupation times $r \mapsto\int_0^\infty {\bf 1}_{B(x,r)}(Y_s)ds$ holds when the process is transient. Then we establish LIL concerning large time behaviors of occupation times $t \mapsto \int_0^t {\bf 1}_{A}(Y_s)ds$ under an additional condition that guarantees the recurrence of the process. Our results cover a large class of Feller (Levy-like) processes, random conductance models with long range jumps, jump processes with mixed polynomial local growths and jump processes with singular jumping kernels.
