Maximal inequality of Stochastic convolution driven by compensated Poisson random measures in Banach spaces

Let $(E, \| \cdot\|)$ be a Banach space such that, for some $q\geq 2$, the function $x\mapsto \|x\|^q$ is of $C^2$ class and its first and second Fr\'{e}chet derivatives are bounded by some constant multiples of $(q-1)$-th power of the norm and $(q-2)$-th power of the norm and let $S$ be a $C_0$-semigroup of contraction type on $(E, \| \cdot\|)$. We consider the following stochastic convolution process \begin{align*} u(t)=\int_0^t\int_ZS(t-s)\xi(s,z)\,\tilde{N}(\mathrm{d} s,\mathrm{d} z), \;\;\; t\geq 0, \end{align*} where $\tilde{N}$ is a compensated Poisson random measure on a measurable space $(Z,\mathcal{Z})$ and $\xi:[0,\infty)\times\Omega\times Z\rightarrow E$ is an $\mathbb{F}\otimes \mathcal{Z}$-predictable function. We prove that there exists a c\`{a}dl\`{a}g modification a $\tilde{u}$ of the process $u$ which satisfies the following maximal inequality \begin{align*} \mathbb{E} \sup_{0\leq s\leq t} \|\tilde{u}(s)\|^{q^\prime}\leq C\ \mathbb{E} \left(\int_0^t\int_Z \|\xi(s,z) \|^{p}\,N(\mathrm{d} s,\mathrm{d} z)\right)^{\frac{q^\prime}{p}}, \end{align*} for all $q^\prime \geq q$ and $1<p\leq 2$ with $C=C(q,p)$.Comment: This version is only very slightly updated as compared to the one from September 201

The Technical Vocabulary Of Newspapers

A seven-million-word newspaper corpus that was made up of approximately 7,600 newspaper articles posted to The New York Times website between June, 2015 and October, 2016 was created and analyzed to identify the technical vocabulary of a newspaper and determine its lexical coverage. The results showed that there were 405 technical words of the newspaper as a whole that accounted for 9.76% of the running words in the NYT corpus, and an average of 748 technical words of each newspaper section with an average lexical coverage of 23.82%. Identifying the technical vocabulary of a newspaper is valuable for language learners, because leaning these words before reading articles may help to reduce the vocabulary burden. The findings also indicated that reading newspapers from the same section is likely to be more effective to learn vocabulary than reading articles randomly

A study of SPDEs w.r.t. compensated Poisson random measures and related topics

This thesis consists of two parts. In the first part, we define stochastic integrals w.r.t. the compensated Poisson random measures in a martingale type p, 1 ≤ p ≤ 2 Banach space and establish a certain continuity, in substitution of the Ita isometry property, for the stochastic integrals .. A version of Ita formula, as a generalization of the case studies in Ikecla and Watanabe [40], is derived. This Itô formula enables us to treat certain Levy processes without Gaussion components. Moreover, using ideas in [63] a version of stochastic Fubini theorem for stochastic integrals W.r. t. compensated Poisson random measures in martingale type spaces is established. In addition, if we assume that E is a martingale type p Banach space with the q-th, q ≥ p, power of the norm in C2-class, then we prove a maximal inequality for a cadlag modification u of the stochastic convolution w.r.t. the compensated Poisson random measures of a contraction Co-semigroups. The second part of this thesis is concerned with the existence and uniqueness of global mild solutions for stochastic beam equations w.r.t. the compensated Poisson random measures. In view of Khas'minskii's test for nonexplosions, the Lyapunov function technique is used via the Yosida approximation approach. Moreover, the asymptotic stability of the zero solution is proved and the Markov property of the solution is verified

Investor Sentiment – Implications from A Repeated Coordination Game Study

We study equilibrium selection in A. Gerber, T. Hens and B. Vogt’s experiment (in Rational Investor Sentiment in a Repeated Stochastic Game with Imperfect Monitoring, 2010), through investigation of subjects’ coordination behaviour and switching behaviour respectively. Quantal choice models are utilized to capture the idiosyncratic component of deviations from the best-response strategy. Our main conclusion is that subjects learn to coordinate through experience of repeated interactions, while their updating beliefs are biased by endogenous expectations systematically. Reference-dependent loss aversion is evidenced. When experiencing gains, i.e. with profit level exceeds endogenous expectation, subjects tend play passively and only follow last period’s realisation of the game. While under the pain of losses, i.e. with lower than expectation profit level, they become more aggressive as the discrepancy between expectation and profit level enlarges; and switch their action even if the game realisation did not switch in last period. Implications for investor sentiment in financial markets are proposed

YOLO-Drone:Airborne real-time detection of dense small objects from high-altitude perspective

Unmanned Aerial Vehicles (UAVs), specifically drones equipped with remote sensing object detection technology, have rapidly gained a broad spectrum of applications and emerged as one of the primary research focuses in the field of computer vision. Although UAV remote sensing systems have the ability to detect various objects, small-scale objects can be challenging to detect reliably due to factors such as object size, image degradation, and real-time limitations. To tackle these issues, a real-time object detection algorithm (YOLO-Drone) is proposed and applied to two new UAV platforms as well as a specific light source (silicon-based golden LED). YOLO-Drone presents several novelties: 1) including a new backbone Darknet59; 2) a new complex feature aggregation module MSPP-FPN that incorporated one spatial pyramid pooling and three atrous spatial pyramid pooling modules; 3) and the use of Generalized Intersection over Union (GIoU) as the loss function. To evaluate performance, two benchmark datasets, UAVDT and VisDrone, along with one homemade dataset acquired at night under silicon-based golden LEDs, are utilized. The experimental results show that, in both UAVDT and VisDrone, the proposed YOLO-Drone outperforms state-of-the-art (SOTA) object detection methods by improving the mAP of 10.13% and 8.59%, respectively. With regards to UAVDT, the YOLO-Drone exhibits both high real-time inference speed of 53 FPS and a maximum mAP of 34.04%. Notably, YOLO-Drone achieves high performance under the silicon-based golden LEDs, with a mAP of up to 87.71%, surpassing the performance of YOLO series under ordinary light sources. To conclude, the proposed YOLO-Drone is a highly effective solution for object detection in UAV applications, particularly for night detection tasks where silicon-based golden light LED technology exhibits significant superiority