Related papers: Asymptotic Stochastic Comparison of Random Process…
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…
We give sufficient conditions for the asymptotic normality of linear combinations of order statistics (L-statistics) in the case of simple random samples without replacement. In the first case, restrictions are imposed on the weights of…
In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
In this paper, we consider asymptotic behaviors of multiscale multivalued stochastic systems with small noises. First of all, for general, fully coupled systems for multivalued stochastic differential equations of slow and fast motions with…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
A central paradigm behind process semantics based on observability and testing is that the exact moment of occurring of an internal nondeterministic choice is unobservable. It is natural, therefore, for this property to hold when the…
Consider $K$ processes, each generating a sequence of identical and independent random variables. The probability measures of these processes have random parameters that must be estimated. Specifically, they share a parameter $\theta$…
We present the formalism of sequential and asynchronous processes defined in terms of random or quantum grammars and argue that these processes have relevance in genomics. To make the article accessible to the non-mathematicians, we keep…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we establish various non-standard central limit theorems. We…
We study the characteristic function and moments of the integer-valued random variable $\lfloor X+\alpha\rfloor$, where $X$ is a continuous random variables. The results can be regarded as exact versions of Sheppard's correction. Rounded…
We extend a general result showing that the asymptotic behavior of high moments, factorial or standard, of random variables, determines the asymptotically normality, from the one dimensional to the multidimensional setting. This approach…
In multi-period stochastic optimization problems, the future optimal decision is a random variable whose distribution depends on the parameters of the optimization problem. We analyze how the expected value of this random variable changes…
The amount of randomness in a signal generated by physical or non-physical process can reveal important information about that process. For example, the presence of randomness in ECG signals may indicate a cardiac disease. On the hand, the…
A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis…
Different stochastic extensions of hybrid automata have been proposed in the past, with unclear expressivity relations between them. To structure and relate these modeling languages, in this paper we formalize two alternative approaches to…
We introduce a class of stochastic processes with reinforcement consisting of a sequence of random partitions $\{\mathcal{P}_t\}_{t \ge 1}$, where $\mathcal{P}_t$ is a partition of $\{1,2,\dots, Rt\}$. At each time~$t$,~$R$ numbers are…
The comparison of local characteristics of two random processes can shed light on periods of time or space at which the processes differ the most. This paper proposes a method that learns about regions with a certain volume, where the…
We address the problem of searching for a change point in an anomalous process among a finite set of M processes. Specifically, we address a composite hypothesis model in which each process generates measurements following a common…