An Invariance Principle for Reduced U-Statistics.
An invariance principle for the law of the iterated logarithm for some Markov chains
Strassen's invariance principle for additive functionals of Markov chains with spectral gap in the Wasserstein metric is proved.
An Invariance Principle for U-Statistics in Simple Random Sampling without Replacement.
An invariance principle in for non stationary -mixing sequences
Invariance principle in is studied using signed random measures. This approach to the problem uses an explicit isometry between and a reproducing kernel Hilbert space giving a very convenient setting for the study of compactness and convergence of the sequence of Donsker functions. As an application, we prove a version of the invariance principle in the case of -mixing random variables. Our result is not available in the -setting.
An invariant sum related to record statistics.
An isomorphic Dvoretzky's theorem for convex bodies
We prove that there exist constants C>0 and 0 < λ < 1 so that for all convex bodies K in with non-empty interior and all integers k so that 1 ≤ k ≤ λn/ln(n+1), there exists a k-dimensional affine subspace Y of satisfying . This formulation of Dvoretzky’s theorem for large dimensional sections is a generalization with a new proof of the result due to Milman and Schechtman for centrally symmetric convex bodies. A sharper estimate holds for the n-dimensional simplex.
An isoperimetric inequality on the ℓp balls
The normalised volume measure on the ℓnp unit ball (1≤p≤2) satisfies the following isoperimetric inequality: the boundary measure of a set of measure a is at least cn1/pãlog1−1/p(1/ã), where ã=min(a, 1−a).
An iterative implementation of the implicit nonlinear filter
Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration method for solving the resulting algebraic equations.
An iterative implementation of the implicit nonlinear filter
Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration method for solving the resulting algebraic equations.
An Itô type isometry for loops in via the brownian bridge
An invariance principle for LPQD random variables.
An queue with close-down and vacation times.
An M/G/1 queueing system with compulsory server vacations.
This paper deals with a single server queue with compulsory server vacations. There are single Poisson arrivals with mean arrival date λ and the service is performed in batches of fixed size M (≥1) or min (n, M) and the service times of successive batches follow a general distribution with the density function D(x). The Laplace transforms of the probability generating functions of different states of the system have been obtained, the corresponding steady state results have been derived and in a...
An MX/G/1 unreliable retrial queue with two phase service and persistence behaviour of customers in service
This paper describes an unreliable server batch arrival retrial queue with two types of repair and second optional service. The server provides preliminary first essential service (FES) to the primary arriving customers or customers from retrial group. On successful completion of FES, the customer may opt for second optional service (SOS) with probability α. The server is subject to active break downs. The customer under FES (or SOS) during the failure decides, with probability q, to join the orbit(impatientcustomer)...
An observation about submatrices.
An occupancy problem with group drawings of different sizes
An Open Mapping Theorem for Measures.
An open toss problem.
An operator for characteristic functions
An operatorial approach to stochastic partial differential equations driven by linear multiplicative noise