Reflected scheme for doubly reflected BSDEs with jumps and RCLL obstacles

We introduce a discrete time reflected scheme to solve doubly reflected Backward Stochastic Differential Equations with jumps (in short DRBSDEs), driven by a Brownian motion and an independent compensated Poisson process. As in Dumitrescu-Labart (2014), we approximate the Brownian motion and the Poisson process by two random walks, but contrary to this paper, we discretize directly the DRBSDE, without using a penalization step. This gives us a fully implementable scheme, which only depends on one parameter of approximation: the number of time steps $n$ (contrary to the scheme proposed in Dumitrescu-Labart (2014), which also depends on the penalization parameter). We prove the convergence of the scheme, and give some numerical examples.Comment: arXiv admin note: text overlap with arXiv:1406.361

Femininity Aspect as Reflected in Lisa See\u27s Snow Flower and the Secret Fan

The purpose of this study is to describe forms opression faced by Chinese women in the nineteenth century as reflected in te novel “Snow Flower and the Secret Fan” written by Lisa See, then to find out the way of the Chinese women to minimize their secluded life. This study is carried out with descriptive research which is collected with documentary technique and used a documentary sheet as the instrument. The finding indicates about the idea of femininity aspect that describes in the oppression faced by Chinese women. This oppression derives into three forms of oppression; emotional oppression, physical oppression, and sexual oppression. The Chinese women try to obey the particular custom judge by the culture to construct the femininity aspect, but secretly they tru to find a way to minimize their secluded life through Nu Shu (secret writing) and having a baby boy. It is hoped that the result of this study will be useful to anyone who wants to study women life situation in a certain communities

Dynamical Symmetries Reflected in Realistic Interactions

Realistic nucleon-nucleon (NN) interactions, derived within the framework of meson theory or more recently in terms of chiral effective field theory, yield new possibilities for achieving a unified microscopic description of atomic nuclei. Based on spectral distribution methods, a comparison of these interactions to a most general Sp(4) dynamically symmetric interaction, which previously we found to reproduce well that part of the interaction that is responsible for shaping pairing-governed isobaric analog 0+ states, can determine the extent to which this significantly simpler model Hamiltonian can be used to obtain an approximate, yet very good description of low-lying nuclear structure. And furthermore, one can apply this model in situations that would otherwise be prohibitive because of the size of the model space. In addition, we introduce a Sp(4) symmetry breaking term by including the quadrupole-quadrupole interaction in the analysis and examining the capacity of this extended model interaction to imitate realistic interactions. This provides a further step towards gaining a better understanding of the underlying foundation of realistic interactions and their ability to reproduce striking features of nuclei such as strong pairing correlations or collective rotational motion.Comment: 10 pages, 4 figures, Proceedings of the XXV International Workshop on Nuclear Theory, June 26-July 1, 2006, Rila Mountains, Bulgari

Discrete approximations to reflected Brownian motion

In this paper we investigate three discrete or semi-discrete approximation schemes for reflected Brownian motion on bounded Euclidean domains. For a class of bounded domains $D$ in $\mathbb{R}^n$ that includes all bounded Lipschitz domains and the von Koch snowflake domain, we show that the laws of both discrete and continuous time simple random walks on $D\cap2^{-k}\mathbb{Z}^n$ moving at the rate $2^{-2k}$ with stationary initial distribution converge weakly in the space $\mathbf{D}([0,1],\mathbb{R}^n)$, equipped with the Skorokhod topology, to the law of the stationary reflected Brownian motion on $D$. We further show that the following ``myopic conditioning'' algorithm generates, in the limit, a reflected Brownian motion on any bounded domain $D$. For every integer $k\geq1$, let $\{X^k_{j2^{-k}},j=0,1,2,...\}$ be a discrete time Markov chain with one-step transition probabilities being the same as those for the Brownian motion in $D$ conditioned not to exit $D$ before time $2^{-k}$. We prove that the laws of $X^k$ converge to that of the reflected Brownian motion on $D$. These approximation schemes give not only new ways of constructing reflected Brownian motion but also implementable algorithms to simulate reflected Brownian motion.Comment: Published in at http://dx.doi.org/10.1214/009117907000000240 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org