相关论文: General Law of iterated logarithm for Markov proce…

Continuing from arXiv:2102.01917v2, in this paper, we discuss general criteria and forms of liminf laws of iterated logarithm (LIL) for continuous-time Markov processes. Under some minimal assumptions, which are weaker than those in…

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…

Based on two-sided heat kernel estimates for a class of symmetric jump processes on metric measure spaces, the laws of the iterated logarithm (LILs) for sample paths, local times and ranges are established. In particular, the LILs are…

The law of the iterated logarithm (LIL) for the time-homogeneous Markov process with a unique invariant measure characterizes the almost sure maximum possible fluctuation of time averages around the ergodic limit. Whether a numerical…

We present sufficient conditions, in terms of the jumping kernels, for two large classes of conservative Markov processes of pure-jump type to be purely discontinuous martingales with finite second moment. As an application, we establish…

This paper explores the Law of the Iterated Logarithm (LIL) for $m$-dependent sequences under the framework of sub-linear expectations. We first extend existing LIL results to sequences of independent, non-identically distributed random…

Let $Y$ be a symmetric Borel right process with locally compact state space $T\subseteq R^{1}$ and potential densities $u(x,y)$ with respect to some $\sigma$-finite measure on $T$. Let $g$ and $f$ be finite excessive functions for $ Y$. Set…

We prove Chung-type laws of the iterated logarithm for general L\'{e}vy processes at zero. In particular, we provide tools to translate small deviation estimates directly into laws of the iterated logarithm. This reveals laws of the…

Suppose that $X=(X_{t})_{t\ge 0}$ is either a general supercritical non-local branching Markov process, or a general supercritical non-local superprocess, on a Luzin space. Here, by ``supercritical" we mean that the mean semigroup of $X$…

The classical law of the iterated logarithm (LIL for short)as fundamental limit theorems in probability theory play an important role in the development of probability theory and its applications. Strassen (1964) extended LIL to large…

We establish integral tests and laws of the iterated logarithm at 0 and at $+\infty$, for the upper envelope of positive self-similar Markov processes. Our arguments are based on the Lamperti representation, time reversal arguments and on…

Let $\{(X_t)_{t\geq 0}, \mathbb{P}_{\delta_x}, x\in E\}$ be a supercritical branching Markov process (which is not necessary symmetric) on a locally compact metric measure space $(E,\mu)$ with spatially dependent local branching mechanism.…

Let X,X_1,X_2,... be independent identically distributed random variables and let h(x,y)=h(y,x) be a measurable function of two variables. It is shown that the bounded law of the iterated logarithm, $\limsup_n (n\log\log n)^{-1}|\sum_{1<=…

In this paper, we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space, where the random variables are not necessarily identically distributed. Exponential…

Let $(\xi_k, \eta_k)_{k\geq 1}$be independent identically distributed random vectors with arbitrarily dependent positive components and $T_k:=\xi_1+\ldots+\xi_{k-1}+\eta_k$for $k\in\mathbb{N}$. We call the random sequence {T_k, k=1,2...} a…

We prove a law of the iterated logarithm (LIL) for an infinite sum of independent indicators parameterized by $t$ as $t\to\infty$. It is shown that if the expectation $b$ and the variance $a$ of the sum are comparable, then the…

We present an It\^o formula for the $L_p$-norm of jump processes having stochastic differentials in $L_p$-spaces. The main results extend well-known theorems of Krylov to the case of processes with jumps, and which can be used to prove…

We establish a law of the iterated logarithm (LIL) for the set of real numbers whose $n$-th partial quotient is bigger than $\alpha_n$, where $(\alpha_n)$ is a sequence such that $\sum 1/\alpha_n$ is finite. This set is shown to have…

In this article, we introduce \textit{Mallows processes}, defined to be continuous-time c\`adl\`ag processes with Mallows distributed marginals. We show that such processes exist and that they can be restricted to have certain natural…

We establish integral tests and laws of the iterated logarithm for the upper envelope of the future infimum of positive self-similar Markov processes and for increasing self-similar Markov processes at 0 and infinity. Our proofs are based…