  In this paper, we discuss general criteria and forms of both liminf and
limsup laws of iterated logarithm (LIL) for continuous-time Markov processes.
We consider minimal assumptions for both LILs to hold at zero (at infinity,
respectively) in general metric measure spaces. We establish LILs under local
assumptions near zero (near infinity, respectively) on uniform bounds of the
first exit time from balls in terms of a function $\phi$ and uniform bounds on
the tails of the jumping measure in terms of a function $\psi$. One of the main
results is that a simple ratio test in terms of the functions $\phi$ and $\psi$
completely determines whether there exists a positive nondecreasing function
$\Psi$ such that $\limsup |X_t|/\Psi(t)$ is positive and finite a.s., or not.
We also provide a general formulation of liminf LIL, which covers jump
processes whose jumping measures have logarithmic tails. Our results cover a
large class of subordinated diffusions, jump processes with mixed polynomial
local growths, jump processes with singular jumping kernels and random
conductance models with long range jumps.
