Related papers: On Convergence to Stochastic Integrals
Finite population inference is a central goal in survey sampling. Probability sampling is the main statistical approach to finite population inference. Challenges arise due to high cost and increasing non-response rates. Data integration…
We consider a generalization of the weighted random ball model. The model is driven by a random Poisson measure with a product heavy tailed intensity measure. Such a model typically represents the transmission of a network of stations with…
We introduce a new formalism for computing expectations of functionals of arbitrary random vectors, by using generalised integration by parts formulae. In doing so we extend recent representation formulae for the score function introduced…
This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…
We prove that if a rectangular matrix with uniformly small entries and approximately orthogonal rows is applied to the independent standardized random variables with uniformly bounded third moments, then the empirical CDF of the resulting…
We study weak convergence of empirical processes of dependent data $(X_i)_{i\geq0}$, indexed by classes of functions. Our results are especially suitable for data arising from dynamical systems and Markov chains, where the central limit…
We study the sequential empirical process indexed by general function classes and its smoothed set-indexed analogue. Sufficient conditions for asymptotic equicontinuity are provided for nonstationary arrays of time series. This yields…
The representation Skorohod theorem of weak convergence of random variables on a metric space goes back to Skorohod (1956) in the case where the metric space is the class of real-valued functions defined on [0,1] which are right-continuous…
Stochastic variance-reduced algorithms such as Stochastic Average Gradient (SAG) and SAGA, and their deterministic counterparts like the Incremental Aggregated Gradient (IAG) method, have been extensively studied in large-scale machine…
Joining records with all other records that meet a linkage condition can result in an astronomically large number of combinations due to many-to-many relationships. For such challenging (acyclic) joins, a random sample over the join result…
A new coupling argument is introduced to establish Driver's integration by parts formula and shift Harnack inequality. Unlike known coupling methods where two marginal processes with different starting points are constructed to move…
This article starts with the fundamental theory of stochastic type convergence and the significance of uniform integrability in the context of expectation value. A novel probabilistic sampling kantorovich (PSK-operators) is established with…
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…
``Orderly divergence'' deals with limit theorems for weighted stochastic Gamma integrals of otherwise nonintegrable functions. Although for monotonic functions this category usually coincides with the classical notion of weighted limit…
We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
Varying domains and biased datasets can lead to differences between the training and the target distributions, known as covariate shift. Current approaches for alleviating this often rely on estimating the ratio of training and target…
We introduce a new regression method that relates the mean of an outcome variable to covariates, under the "adverse condition" that a distress variable falls in its tail. This allows to tailor classical mean regressions to adverse…
In this paper, we first analyze the strong and weak convergence of projective integration methods for multiscale stochastic dynamical systems driven by $\alpha$-stable processes, which are used to estimate the effect that the fast…
Rough paths techniques give the ability to define solutions of stochastic differential equations driven by signals $X$ which are not semimartingales and whose $p$-variation is finite only for large values of $p$. In this context, rough…