In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation, referred to as the rapidly decreasing tempered stable (RDTS) GARCH model. This model allows the description of some stylized empirical facts observed for stock and index returns, such as volatility clustering, the non-zero skewness and excess kurtosis for the residual distribution. Furthermore, we...

We study the direct and inverse spectral problems for semiclassical operators of the form S = S0 + ~V , where S0 = 12 ( −~∆Rn + |x| ) is the harmonic oscillator and V : R → R is a tempered smooth function. We show that the spectrum of S forms eigenvalue clusters as ~ tends to zero, and compute the first two associated “band invariants”. We derive several inverse spectral results for V , under v...

We show that Bowen’s equation, which characterises the Hausdorff dimension of certain sets in terms of the topological pressure of an expanding conformal map, applies in greater generality than has been heretofore established. In particular, we consider an arbitrary subset Z of a compact metric space and require only that the lower Lyapunov exponents be positive on Z, together with a tempered c...

In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold X. Then we define stratified ultradistributions of Beurling and Roumieu type on X. In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if X is a real surface, the tempered...

Tempered fractional derivatives originated from the tempered fractional diffusion equations (TFDEs) modeled on the whole space R (see [?]). For numerically solving TFDEs, two kinds of generalized Laguerre functions were defined and some important properties were proposed to establish the approximate theory. The related prototype tempered fractional differential problems was proposed and solved ...

In this paper we introduce a Langevin-type model of subdiffusion with tempered α-stable waiting times. We consider the case of space-dependent external force fields. The model displays subdiffusive behavior for small times and it converges to standard Gaussian diffusion for large time scales. We derive general properties of tempered anomalous diffusion from the theory of tempered α-stable proce...

We study the G/GI/∞ queue in heavy-traffic using tempered distribution-valued processes which track the age and residual service time of each customer in the system. In both cases, we use the continuous mapping theorem together with functional central limit theorem results in order to obtain fluid and diffusion limits for these processes in the space of tempered distributionvalued processes. We...

Lusztig’s presentation of the graded Hecke algebra in terms of generators and relations allows for the definition of algebras associated to noncrystallographic root systems. The representation theory of general graded Hecke algebras is investigated, the expected number of tempered representations for H(H3) are accounted for, and it is shown that one of these representations has the unexpected p...

We develop a partial trace formula which circumvents some technical difficulties in computing the Selberg trace formula for the quotient SL3(Z)\SL3(R)/SO3(R). As applications, we establish the Weyl asymptotic law for the discrete Laplace spectrum and prove that almost all of its cusp forms are tempered at infinity. The technique shows there are non-lifted cusp forms on SL3(Z)\SL3(R)/SO3(R) as w...

19 Preliminary enthusiasm over the encouraging spectrum and in vitro activity of siderophore conjugates 20 such as MB-1 has recently been tempered by unexpected variability in in vivo efficacy. The need for 21 these conjugates to compete for iron with endogenously-produced siderophores has exposed a 22 significant liability for this novel antibacterial strategy. Here, we have exploited dependen...