Weak uniqueness and density estimates for sdes with coefficients depending on some path-functionals

In this paper, we develop a general methodology to prove weak uniqueness for stochastic differential equations with coefficients depending on some path-functionals of the process. As an extension of the technique developed by Bass \& Perkins [BP09] in the standard diffusion case, the proposed methodology allows one to deal with processes whose probability laws are singular with respect to the Lebesgue measure. To illustrate our methodology, we prove weak existence and uniqueness in two examples : a diffusion process with coefficients depending on its running symmetric local time and a diffusion process with coefficients depending on its running maximum. In each example, we also prove the existence of the associated transition density and establish some Gaussian upper-estimates

Predicting Online Invitation Responses with a Competing Risk Model Using Privacy-Friendly Social Event Data

Predicting people's responses to invitations is an important issue for social event management, as the decision-making process behind member responses to invitations is complicated. The purpose of this paper is to suggest a privacy-friendly method to predict whether and when people will respond to open invitations. We apply the competing risk model to predict member responses. The predictive model uses past social event participation data to infer a network structure among people who accept or reject invitations. The inferred networks collectively show the extent to which people are likely to accept or reject invitations. Validated using real datasets including 31,230 people and 8,885 events, the proposed method not only presents the variables that predict attendance (such as past attendance and social network), but also those that predict faster responses. This approach is privacy friendly, as it requires no personal information regarding people and social events (such as name, age and gender or event content). This work contributes to the predictive modeling literature as the first study of a competing risk model developed for replies to a social invitation. Our findings will help event organizers predict how many people will attend events, allowing them to organize effectively

Inflationary Effect of Oil-Price Shocks in an Imperfect Market: A Partial Transmission Input-output Analysis

This paper aims to examine the impacts of oil-price shocks on China’s price levels. To that end, we develop a partial transmission input-output model that captures the uniqueness of the Chinese market. We hypothesize and simulate price control, market factors and technology substitution - the three main factors that restrict the functioning of a price pass-through mechanism during oil-price shocks. Using the models of both China and the U.S., we separate the impact of price control from those of other factors leading to China’s price stickiness under oil-price shocks. The results show a sharp contrast between China and the U.S., with price control in China significantly preventing oil-price shocks from spreading into its domestic inflation, especially in the short term. However, in order to strengthen the economy’s resilience to oil-price shocks, the paper suggests a gradual relaxing of price control in China.Oil-price Shocks, Price Transmission, Price Control, Input-output Analysis, Inflation, Industrial Structure, China, the United States

Charmless decays B -> PP, PV, and effects of new strong and electroweak penguins in Topcolor-assisted Technicolor model

Based on the low energy effective Hamiltonian with generalized factorization, we calculate the new physics contributions to the branching ratios and CP-violating asymmetries of the two-body charmless hadronic decays $B \to PP, PV$ from the new strong and electroweak penguin diagrams in the TC2 model. The top-pion penguins dominate the new physics corrections, and both new gluonic and electroweak penguins contribute effectively to most decay modes. For tree-dominated decay modes $B \to \pi \pi, \rho \pi, etc,$ the new physics corrections are less than 10%. For decays $B \to K^{(*)} \pi$, $K^{(*)} \eta$, $etc$, the new physics enhancements can be rather large (from $- 70$ to $\sim 200$) and are insensitive to the variations of $N_c^{eff}$, $k^2$, $\eta$ and $m_{\tilde{\pi}}$ within the reasonable ranges. For decays $B^0 \to \phi \pi$, $\phi \eta^{(')}$, $K^* \bar{K}^0$ and $\rho^+ K^0$, $\delta {\cal B}$ is strongly $N_c^{eff}-$dependent: varying from -90% to $\sim 1680$ in the range of $N_c^{eff}=2-\infty$. The new physics corrections to the CP-violating asymmetries ${\cal A}_{CP}$ vary greatly for different B decay channels. For five measured CP asymmetries of $B \to K \pi, K \eta', \omega \pi$ decays, $\delta {\cal A}_{CP}$ is only about 20% and will be masked by large theoretical uncertainties. The new physics enhancements to interesting $B \to K \eta'$ decays are significant in size ($\sim 50$), insensitive to the variations of input parameters and hence lead to a plausible interpretation for the unexpectedly large $B \to K \eta'$ decay rates. The TC2 model predictions for branching ratios and CP-violating asymmteries of all fifty seven $B \to PP, PV$ decay modes are consistent with the available data within one or two standard deviations.Comment: Latex file, 56 pages with 11 ps and eps figures. to be published in Eur.Phys.J.