Related papers: High minima of non-smooth Gaussian processes
We find the logarithmic small ball asymptotics for the $L_2$-norm with respect to a degenerate self-similar measures of a certain class of Gaussian processes including Brownian motion, Ornstein - Uhlenbeck process and their integrated…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
In this paper, for centered homogeneous Gaussian random fields the joint limiting distributions of normalized maxima and minima over continuous time and uniform grids are investigated. It is shown that maxima and minima are asymptotic…
We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also…
This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning…
We consider the problem of `discrete-time persistence', which deals with the zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T = n(\Delta T). For a Gaussian Stationary Process the persistence (no…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
Gaussian random fields on finite dimensional smooth manifolds whose variances reach their maximum value at smooth submanifolds are considered. Exact asymptotic behaviors of large excursion probabilities have been evaluated. Vector Gaussian…
The sharp asymptotics for the L^2-quantization errors of Gaussian measures on a Hilbert space and, in particular, for Gaussian processes is derived. The condition imposed is regular variation of the eigenvalues.
We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling property as standard Brownian motion and plays an important role in the study…
We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…
A celebrated result by Gordon allows one to compare the min-max behavior of two Gaussian processes if certain inequality conditions are met. The consequences of this result include the Gaussian min-max (GMT) and convex Gaussian min-max…
We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…
The paper deals with the asymptotic laws of functional of standard random variables. These classes of statistics are closely related to estimators of the extreme value index when the underlying distribution function is in the Weibull domain…
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…
The problem is a power-law asymptotics of the probability that a self-similar process does not exceed a fixed level during long time. The exponent in such asymptotics is estimated for some Gaussian processes, including the fractional…
The pseudo-marginal algorithm is a variant of the Metropolis--Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density.…
Gaussian random processes which variances reach theirs maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximums of theirs trajectories have been evaluated using Double Sum Method…
Two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations. A number of asymptotic results addressing these problems over a fixed…
In this paper, we investigate first the asymptotics of the minima of elliptical triangular arrays. Motivated by the findings of Kabluchko (Extremes 14 (2011) 285-310), we discuss further the asymptotic behaviour of the maxima of elliptical…