This paper treats model reduction of linear time-varying models in continuous time. The method proposed is based on time-varying Lyapunov inequalities and balancing of Gramians. An error bound for truncated models that generalizes the well-known ’twicethe-sum-of-the-tail’-formulafor time-invariant balanced systems is obtained. Input-output stability of truncated balanced models is also proved.

Continuous time random walks incorporate a random waiting time between random jumps. They are used in physics to model particle motion. When the time between particle jumps has a slowly varying probability tail, the resulting plume disperses at a slowly varying rate. The limiting stochastic process is useful for modeling ultraslow diffusion in physics.

The caption for Figure 5 reads: One-color SNV quantification. (A) Primers are designed with the single nucleotide variant at the 3′ end of the complementary region. Noncomplementary tails of varying lengths are then added to the 5′ end and amplified with a universal reverse primer. (B) 1:4 mixture of MUT/WT BRAF template amplified with mutant primers with the short tail and wild-type primers wi...

The Gaussian arbitrarily varying channel with input constraint r and state constraint 2 admits input sequences x = ( x l , , x , ~ ) of real numbers with Cxf 5 nT and state sequences s = ( 5 ,. , T , ~ ) of real numbers with L Y ~ 5 H A ; the output sequence x + s + V , where V = ( VI, , y , ) is a sequence of independent and identically distributed Gaussian random variables with mean 0 and var...

Random network models generated using sparse exchangeable graphs have provided a mechanism to study wide variety of complex real-life networks. In particular, these help with investigating power-law properties degree distributions, number edges, and other relevant metrics which support the scale-free structure Previous work on such imposes marginal assumption univariate regular variation (e.g.,...

This paper investigates co-movements among the Chinese stock market, Shanghai International Energy Exchange (INE) crude oil futures and West Texas Intermediate (WTI) futures. We use Copula models to capture tail dependencies employ VAR-BEKK-GARCH model examine direction of volatility spillovers. find that there are positively time-varying dependency relationships three markets. Compared with co...

Computation of extreme quantiles and tail-based risk measures using standard Monte Carlo simulation can be inefficient. A method to speed up computations is provided by importance sampling. We show that importance sampling algorithms, designed for efficient tail probability estimation, can significantly improve Monte Carlo estimators of tail-based risk measures. In the heavy-tailed setting, whe...

We consider the problem of sampling paths of a random walk up to the first time it crosses a fixed barrier, in the setting where the step sizes are iid with negative mean and have a regularly varying right tail. We study the efficiency of an AcceptanceRejection-type of simulation algorithm that is based on the change of measure proposed by Blanchet and Glynn [9]. We show that this algorithm is ...

We consider a nearly unstable, or near unit root, AR(1) process with regularly varying innovations. Two different approximations for the stationary distribution of such processes exist: a Gaussian approximation arising from the nearly unstable nature of the process and a heavy-tail approximation related to the tail asymptotics of the innovations. We combine these two approximations to obtain a ...

A detailed analytical and numerical study of the suppression of the transverse head-tail instability by modulating the chromaticity over a synchrotron period is presented. We find that a threshold can be developed, and it can be increased to a value larger than the strong head-tail instability threshold. The stability criterion derived agrees very well with the simulations. The underlying physi...