where the terminal condition ξ and the coefficient g = g(t, y, z) are given. W is a d–dimensional Brownian motion. The solution (yt, zt)t∈[0,T ] is a pair of square integrable processes. A foundational and interesting problem is: what is the relationship between the uniqueness of solution and continuous dependence with respect to g or ξ? In the standard situation where g satisfies linear growth...

This vignette is a slightly modified version of Koenker (2008a). It was written in plain latex not Sweave, but all data and code for the examples described in the text are available from either the JSS website or from my webpages. Quantile regression for censored survival (duration) data offers a more flexible alternative to the Cox proportional hazard model for some applications. We describe t...

The sequences, or primary structures, of existing biopolymers--in particular, proteins--are believed to be a product of evolution. Are the sequences random? If not, what is the character of this nonrandomness? To explore the statistics of protein sequences, we use the idea of mapping the sequence onto the trajectory of a random walk, originally proposed by Peng et al. [Peng, C.-K., Buldyrev, S....

This paper presents ECOLE, a look-ahead text editor that supports authors writing seemingly informal specifications in PENG, a computer-processable controlled natural language. ECOLE communicates via a socket interface with the controlled language processor of the PENG system. After each word form entered the lookahead editor displays appropriate lookahead categories. These syntactic hints tell...

This paper shows how a controlled natural language can be used to construct precise formal representations for reasoning about events and their effects. Specifications written in PENG Light are translated with the help of discourse representation structures into the input language of the Simplified Event Calculus. This logic-based formalism is declarative and can be used for various reasoning t...

In the probability literature, backward stochastic differential equations (BSDE) received considerable attention after their introduction by E. Pardoux and S. Peng [5, 6] in 1990. During the past decade, interesting connections to partial differential equations (PDE) were obtained and the theory found wide applications in mathematical finance. The key property of the BSDE’s is the random termin...

The peng-Robinson (PR), a cubic equation of state (EoS), is extended to polymers by using a single set of energy (A1, A2, A3) and co-volume (b) parameters per polymer fitted to experimental volume data. Excellent results for the volumetric behavior of the 11 polymer up to 2000 bar pressure are obtained. The EoS is applied to the correlation and prediction of Henry constants in polymer solutions...

The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusions with set-valued maximal monotone mappings and inverse-strongly monotone mappings, and the set of fixed points of a family of finitely nonexpansive mappings in the setting of Hilbert spaces. We propose a new...