<p style='text-indent:20px;'>We study the stochastic stability in zero-noise limit from a quantitative point of view.</p><p consider smooth expanding maps circle perturbed by additive noise. We show that this case has quadratic speed convergence, as suggested numerical experiments and heuristics published Lin, 2005 (see [<xref ref-type="bibr" rid="b25">25</xref>]). Th...

We study non-Gaussian fractional stochastic volatility models. The in such a model is described by positive function of process that transform the solution to an SDE satisfying Yamada–Watanabe condition. Such models are generalizations version Heston considered Bäuerle and Desmettre (2020). establish sample path small-noise large deviation principles for log-price model. also illustrate how com...

The modulation response, relative intensity noise (RIN) and frequency noise (FN) characteristics of quantum dot (QD) lasers are investigated theoretically in the presence of an external optical beam. Using small signal analysis of the rate equations for carriers and photons, it is demonstrated that by injecting excess carriers into the QDs excited state through optical pumping, the modulation r...

We study the EFT likelihood for biased tracers in redshift space, which bias expansion of galaxy velocity field $\mathbf{v}_g$ plays a fundamental role. The equivalence principle forbids stochastic contributions to survive at small $k$. Therefore, leading order derivatives form ${\cal P}[\tilde{\delta}_g|\delta,\!\mathbf{v}]$ observe redshift-space overdensity $\tilde{\delta}_g(\tilde{\mathbf{x...

In a visual cryptography scheme, a secret image is encoded into n shares, in the form of transparencies. The shares are then distributed to n participants. Qualified subsets of participants can recover the secret image by superimposing their transparencies, but non-qualified subsets of participants have no information about the secret image. Pixel expansion, which represents the number of subpi...

The Boltzmann transport equation is commonly considered to be the best semi-classical description of carrier transport in semiconductors, providing precise information about the distribution of carriers with respect to time (one dimension), location (three dimensions), and momentum (three dimensions). However, numerical solutions for the seven-dimensional carrier distribution functions are very...

We show that any spatially separated multi-part quantum device demonstrating nonlocality can be used in an untrusted-device protocol for randomness expansion with unconditional quantum security. A consequence is that the noise tolerance for secure randomness expansion only needs to be small enough that it rules out deterministic behavior of the device. This greatly reduces the requirement on im...

This paper examines the inter-relationship of three major phenomena- population growth, uncontrolled urban expansion and urban development in Ado Ekiti, Nigeria. Uncontrolled urban expansion has a resultant effect on the urban development of a city whereas uncontrolled urban development is caused by uncontrolled population increase is caused by Migration. This work encapsulates how population g...