arXiv subjects

Zhiyuan Zhang

Publications and source records attributed to Zhiyuan Zhang.

189 records · Page 11Linked to original sources

arXiv2017

An effective version of Katok's horseshoe theorem for conservative $C^2$ surface diffeomorphisms

For area preserving $C^2$ surface diffeomorphisms, we give an explicit finite information condition, on the exponential growth of the number of Bowen's $(n,δ)-$balls needed to cover a positive proportion of the space, that is sufficient to guarantee positive topological entropy. This can be seen as an effective version of Katok's horseshoe theorem in the conservative setting. We also show that the analogous result is false in dimension larger than $3$.

math.DS↗

arXiv2017

On stable transitivity of finitely generated groups of volume preserving diffeomorphisms

In this paper, we provide a new criterion for the stable transitivity of volume preserving finite generated group on any compact Riemannian manifold. As one of our applications, we generalised a result of Dolgopyat and Krikorian in \cite{DK} and obtained stable transitivity for random rotations on the sphere in any dimension. As another application, we showed that for $\infty \geq r \geq 2$, any $C^r$ volume preserving partially hyperbolic diffeomorphism $g$ on any compact Riemannian manifold $M$ having sufficiently Hölder stable or unstable distribution, for any sufficiently large integer $K$, for any $(f_i)_{i=1}^{K}$ in a $C^1$ open $C^r$ dense subset of $\textnormal{\Diff}^r(M,m)^K$, the group generated by $g, f_1,\cdots, f_K$ acts transitively.

math.DS↗

arXiv2016

Electronic structure contribution to hydrogen bonding interaction of a water dimer

Hydrogen bond (H-bond) covalency has recently been observed in ice and liquid water, while the penetrating molecular orbitals (MOs) in the H-bond region of most typical water dimer system, (H2O)2, have also been discovered. However, obtaining the quantitative contribution of these MOs to the H-bond interaction is still problematic. In this work, we introduced the orbital-resolved electron density projected integral (EDPI) along the H-bond to approach this problem. The calculations show that, surprisingly, the electronic occupied orbital (HOMO-4) of (H2O)2 accounts for about 40% of the electron density at the bond critical point. Moreover, the charge transfer analysis visualizes the electron accumulating effect of the orbital interaction within the H-bond between water molecules, supporting its covalent-like character. Our work expands the classical understanding of H-bond with specific contributions from certain MOs, and will also advance further research into such covalency and offer quantitative electronic structure insights into intermolecular systems.

physics.atm-clus↗

arXiv2016

Ballistic Transport and Absolute Continuity of One-Frequency Schrödinger Operators

For the solution $u(t)$ to the discrete Schrödinger equation $${\rm i}\frac{d}{dt}u_n(t)=-(u_{n+1}(t)+u_{n-1}(t))+V(θ+ nα)u_n(t), \quad n\in\Z,$$ with $α\in\R\setminus\Q$ and $V\in C^ω(\T,\R)$, we consider the growth rate with $t$ of its diffusion norm $\langle u(t)\rangle_{p}:=\left(\sum_{n\in\Z}(n^{p}+1) |u_n(t)|^2\right)^\frac12$, and the (non-averaged) transport exponents $$β_u^{+}(p) := \limsup_{t \to \infty} \frac{2\log \langle u(t)\rangle_{p}}{p\log t}, \quad β_u^{-}(p):= \liminf_{t \to \infty} \frac{2\log \langle u(t)\rangle_{p}}{p\log t}.$$ We will show that, if the corresponding Schrödinger operator has purely absolutely continuous spectrum, then $β_{u}^{\pm}(p)=1$, provided that $u(0)$ is well localized.

math.DS↗

arXiv2015

A new method of energy calibration of position-sensitive silicon detector

An improved method of energy calibration of position-sensitive silicon detector is presented. Instead of the parabolic function used in traditional method, a new function describing the relation of position and energy is introduced and achieves better energy resolution. For the 8.088 MeV alpha decay of 213Rn calibrated by this new method, the energy resolution is determined to be about 87 keV (FWHM), which is better than the result of the traditional method, 104 keV (FWHM). In addition, different functions can be tried in the new method, which makes the calibration of various detectors with different performances possible.

physics.ins-det↗

arXiv2015

On the spectrums of ergodic Schrodinger operators with finitely valued potentials

We show that the measure of the spectrum of Schrödinger operator with potential defined by non-constant function over any minimal aperiodic finite subshift tends to zero, as the coupling constant tends to infinity. We also obtained a quantitative upper bound for the measure of the spectrum. This follows from a result we proved for ergodic Schrödinger operators with finitely valued potentials under two conditions on the recurrence property of the shift. We also show that one of these conditions is necessary for such result.

math.DS↗

arXiv2013

Exact simulation pricing with Gamma processes and their extensions

Exact path simulation of the underlying state variable is of great practical importance in simulating prices of financial derivatives or their sensitivities when there are no analytical solutions for their pricing formulas. However, in general, the complex dependence structure inherent in most nontrivial stochastic volatility (SV) models makes exact simulation difficult. In this paper, we present a nontrivial SV model that parallels the notable Heston SV model in the sense of admitting exact path simulation as studied by Broadie and Kaya. The instantaneous volatility process of the proposed model is driven by a Gamma process. Extensions to the model including superposition of independent instantaneous volatility processes are studied. Numerical results show that the proposed model outperforms the Heston model and two other Lévy driven SV models in terms of model fit to the real option data. The ability to exactly simulate some of the path-dependent derivative prices is emphasized. Moreover, this is the first instance where an infinite-activity volatility process can be applied exactly in such pricing contexts.

q-fin.CP↗

arXiv2013

Volatility Inference in the Presence of Both Endogenous Time and Microstructure Noise

In this article we consider the volatility inference in the presence of both market microstructure noise and endogenous time. Estimators of the integrated volatility in such a setting are proposed, and their asymptotic properties are studied. Our proposed estimator is compared with the existing popular volatility estimators via numerical studies. The results show that our estimator can have substantially better performance when time endogeneity exists.

q-fin.ST↗

arXiv2011

Quantile clocks

Quantile clocks are defined as convolutions of subordinators $L$, with quantile functions of positive random variables. We show that quantile clocks can be chosen to be strictly increasing and continuous and discuss their practical modeling advantages as business activity times in models for asset prices. We show that the marginal distributions of a quantile clock, at each fixed time, equate with the marginal distribution of a single subordinator. Moreover, we show that there are many quantile clocks where one can specify $L$, such that their marginal distributions have a desired law in the class of generalized $s$-self decomposable distributions, and in particular the class of self-decomposable distributions. The development of these results involves elements of distribution theory for specific classes of infinitely divisible random variables and also decompositions of a gamma subordinator, that is of independent interest. As applications, we construct many price models that have continuous trajectories, exhibit volatility clustering and have marginal distributions that are equivalent to those of quite general exponential Lévy price models. In particular, we provide explicit details for continuous processes whose marginals equate with the popular VG, CGMY and NIG price models. We also show how to perfectly sample the marginal distributions of more general classes of convoluted subordinators when $L$ is in a sub-class of generalized gamma convolutions, which is relevant for pricing of European style options.

math.PR↗