相关论文: Sharp probability estimates for generalized Smirno…
We study functions g_{\alpha}(x) which are one-sided, heavy-tailed Levy stable probability distributions of index \alpha, 0< \alpha <1, of fundamental importance in random systems, for anomalous diffusion and fractional kinetics. We furnish…
Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…
This paper deals with (finite or infinite) sequences of arbitrary independent events in some probability space. We find sharp lower bounds for the probability of a union of such events when the sum of their probabilities is given. The…
We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…
We elaborate the notions of Martin-L\"of and Schnorr randomness for real numbers in terms of uniform distribution of sequences. We give a necessary condition for a real number to be Schnorr random expressed in terms of classical uniform…
Consider n unit intervals, say [1,2], [3,4], ..., [2n-1,2n]. Identify their endpoints in pairs at random, with all (2n-1)!! = (2n-1) (2n-3) ... 3 1 pairings being equally likely. The result is a collection of cycles of various lengths, and…
We prove existence of (at most denumerable many) absolutely continuous invariant probability measures for random one-dimensional dynamical systems with asymptotic expansion. If the rate of expansion (Lyapunov exponents) is bounded away from…
We present an approximate calculation for the distribution of the maximum of a smooth stationary temporal signal X(t). As an application, we compute the persistence exponent associated to the probability that the process remains below a…
Let $\Theta^{(n)}$ be a random vector uniformly distributed on the unit sphere $\mathbb S^{n-1}$ in $\mathbb R^n$. Consider the projection of the uniform distribution on the cube $[-1,1]^n$ to the line spanned by $\Theta^{(n)}$. The…
In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the…
Let S_i be a random walk with standard exponential increments. We call \sum_{i=1}^k S_i its k-step area. The random variable V = \inf_{k \ge 1} \frac{2}{k(k+1)} \sum_{i=1}^k S_i plays important role in the study of so-called one-dimensional…
The statistical properties of finite-time Lyapunov exponents at the Ulam point of the logistic map are investigated. The exact analytical expression for the autocorrelation function of one-step Lyapunov exponents is obtained, allowing the…
We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically…
We outline some simple prescriptions to define a distribution on the set $\mathbb{Q}_0$ of all the rational numbers in $[0,1]$, and we then explore both a few properties of these distributions, and the possibility of making these rational…
The distribution of the sum of r-th power of standard normal random variables is a generalization of the chi-squared distribution. In this paper, we represent the probability density function of the random variable by an one-dimensional…
Non-uniform estimates are obtained for Poisson, compound Poisson, translated Poisson, negative binomial and binomial approximations to sums of of m-dependent integer-valued random variables. Estimates for Wasserstein metric also follow…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous…
We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the…
Empirical likelihood approach is one of non-parametric statistical methods, which is applied to the hypothesis testing or construction of confidence regions for pivotal unknown quantities. This method has been applied to the case of…
In the present paper we establish a clear correspondence between probabilities of certain edges belonging to a realization of the uniform spanning tree (UST), and the states of a fermionic Gaussian free field. Namely, we express the…