We consider a closed fork and join queueing network where several lines feed a single assembly station. Under the assumption that at least one service time distribution is subexponential, we obtain the tail asymptotics of transient cycle times and waiting times. We also discuss under which conditions these results can be generalized to the tail asymptotics of stationary cycle times and waiting ...

In this paper, we examine the small time-to-expiry behaviour of implied volatility in models of exponential Lévy type. In the at-the-money case, it turns out that the implied volatility converges, as time-to-expiry goes to zero, to the square root of the Gaussian member of the driving Lévy process’ characteristic triplet. In particular, the limit is zero if the Lévy process has no Gaussian part...

We study the firstand second-order asymptotics of covert communication with Pulse-Position Modulation (PPM) over binary-input Discrete Memoryless Channels (DMCs) for three different metrics of covertness. When covertness is measured in terms of the relative entropy between the channel output distributions induced with and without communication, we characterize the exact PPM second-order asympto...

We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a two-dimensional queue-length process. The tail asymptotics have been well studied for two-dimensional reflecting processes where jumps have either a bounded or an unbounded light-tailed distribution. However, p...

The problem of recovering the asymptotics of a short range perturbation of the Euclidean metric on R n from xed energy scattering data is studied. It is shown that if two such metrics, g 1 ; g 2 ; have scattering data at some xed energy which are equal up to smoothing, then there exists a diieomorphism`` xing innnity' such that g 1 g 2 is rapidly decreasing. Given the scattering matrix at two e...

We investigate the probability distribution of Conley-Zehnder indices associated with Brownian random paths on Sp(2n,R) that start at the identity. In the case of n = 1, we prove that the distribution has the same moment asymptotics as the standard random walk on the real line. We also present numerical evidence suggesting that the same asymptotics should hold for general n.

We sharpen a classical result on the spectral asymptotics of the boundary value problems for self-adjoint ordinary differential operator. Using this result we obtain the exact L2-small ball asymptotics for a new class of zero mean Gaussian processes. This class includes, in particular, integrated generalized Slepian process, integrated centered Wiener process and integrated centered Brownian br...

We consider a perturbed system of exponents { en } n∈Z, when the sequence {λn }n∈Z has a definite asymptotics. We study basis properties (completeness, minimality, basicity) of this system in Lebesgue space of functions Lp(·) (−π, π) with variable summability exponent p(·), subject to parameters contained in the asymptotics {λn}n∈Z.

We describe the asymptotics of the spectral norm of finite Toeplitz matrices generated by functions with Fisher-Hartwig singularities as the matrix dimension goes to infinity. In the case of positive generating functions, our result provides the asymptotics of the largest eigenvalue, which is of interest in time series with long-range memory.