Related papers: Asymptotic Stochastic Comparison of Random Process…
We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks that admit tunable (power law) degree distribution and assortativity and clustering coefficients. We show the asymptotic degree…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…
Asymptotic notations are heavily used while analysing runtimes of algorithms. Present paper argues that some of these usages are non trivial, therefore incurring errors in communication of ideas. After careful reconsidera- tion of the…
In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map…
We show that asymptotic equivalence, in a strong form, holds between two random graph models with slightly differing edge probabilities under substantially weaker conditions than what might naively be expected. One application is a simple…
In some inferential statistical methods, such as tests and confidence intervals, it is important to describe the stochastic behavior of statistical functionals, aside from their large sample properties. We study such behavior in terms of…
The asymptotic behavior of a stochastic network represented by a birth and death processes of particles on a compact state space is analyzed. Births: Particles are created at rate $\lambda_+$ and their location is independent of the current…
The paper compares probabilistic and exact methods for estimating the asymptotic behavior of summation arithmetic functions, and estimates of the results are obtained by precise methods. Conditions for stationarity in the broad sense are…
In this short note, we try to provide the reader with a brief pedagogical account of some similarities and differences between stochastic and deterministic processes. A short presentation of some basic notions related to the mathematical…
We aim to link random fields and marked point processes and therefore introduce a new class of stochastic processes which are defined on a random set in R^d. Unlike for random fields, the mark covariance function of a marked random set is…
We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence…
A determinantal approximation is obtained for the permanent of a doubly stochastic matrix. For moderate-deviation matrix sequences, the asymptotic relative error is of order $O(n^{-1})$.
We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…
We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes.…
In this paper, we investigate the asymptotic error distributions of symplectic methods for stochastic Hamiltonian systems and further provide Hamiltonian-specific analysis that clarifies the superiority of symplectic methods. Our…
In this paper the asymptotic distribution of estimators is derived in a general regression setting where rank restrictions on a submatrix of the coefficient matrix are imposed and the regressors can include stationary or I(1) processes.…
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…
Motion of particles (bodies) in presence of random effects can be considered stochastic process. However, application of widely known stochastic processes used for description of particle motion is reduced to relatively small class of…
We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order…