A law of the iterated logarithm for the sample covariance matrix.
A Lemma on Proximity of Variances and Expectations
We define a notion of delta-variance maximization and show it implies epsilon-proximity in expactations.
A lemma on proximity of variances and expectations
A limit law for random walk in a random environment
A limit law for the root value of minimax trees.
A limit theorem for functionals of a Poisson process
A limit theorem for joint distribution of order-statistics from stationary Gaussian sequences
A limit theorem for maxima of nonstationary Gaussian sequences
A limit theorem for the moment of self-normalized sums.
A limit theorem for the position of a particle in the Lorentz model.
A limit theorem for the prediction process under absolute continuity
A limit theorem for the q-convolution
The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative...
A limit theorem for the Riemann zeta-function in the complex space
A limit theorem for the Riemann zeta-function near the critical line in the complex space
A limited queuing problem with any number of arrivals and departures
A limiting distribution for quicksort
A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients.
A linear programming approach to error bounds for random walks in the quarter-plane
We consider the steady-state behavior of random walks in the quarter-plane, in particular, the expected value of performance measures that are component-wise linear over the state space. Since the stationary distribution of a random walk is in general not readily available we establish upper and lower bounds on performance in terms of another random walk with perturbed transition probabilities, for which the stationary distribution is a geometric product-form. The Markov reward approach as developed...
A Littlewood-Paley-Stein estimate on graphs and groups
We establish the boundedness in spaces, 1 < q ≤ 2, of a “vertical” Littlewood-Paley-Stein operator associated with a reversible random walk on a graph. This result extends to certain non-reversible random walks, including centered random walks on any finitely generated discrete group.
A local convergence theorem for partial sums of stochastic adapted sequences
In this paper we establish a new local convergence theorem for partial sums of arbitrary stochastic adapted sequences. As corollaries, we generalize some recently obtained results and prove a limit theorem for the entropy density of an arbitrary information source, which is an extension of case of nonhomogeneous Markov chains.