Continuous Time Models

According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function, the entropy potential. The validity and the consequences of this hypothesis are explored in detail. The numerical investigation of a continuous-time model provides a further confirmation to the existence of the entropy potential. Furthermore, it is shown that the knowledge of the entropy potential allows determining also Lyapunov spectra in general reference frames where the time-like and space-like axes point along generic directions in the space-time plane. Finally, the existence of an entropy potential implies that the integrated density of positive exponents ͑Kolmogorov-Sinai entropy͒ is independent of the chosen reference frame. © 1997 American Institute of Physics. ͓S1054-1500͑97͒02704-3͔ Out-of-equilibrium systems give rise to a rich variety of phenomena that are often dealt with using ad hoc methods. Perhaps the main...

In this paper we investigate a continuous time autoregressive moving- average model (CARMA) for the instantaneous spot interest rate. This model can be interpreted as a generalized Vasicek (1977) model where higher order lags and moving average terms are allowed in the spot rate dynamics. Our model fit in the general ane class of term structure models, and we provide

In this paper we compare the forecast performance of continuous and discrete-time volatility models. In discrete time, we consider more than ten GARCH-type models and an asymmetric autoregressive stochastic volatility model. In continuous-time, a stochastic ...

Merton's famous continuous-time model of optimal consumption and investment is extended to allow for a wage earner to have a random lifetime and to use a portion of the income to purchase life insurance in order to provide for his or her estate. With constant relative risk aversion utility functions, the wage earner's problem is to flnd the optimal consumption,

Abstract Q-learning is a technique used to compute an optimal policy for a controlled Markov chain based on observations of the system controlled using a non-optimal policy. It has proven to be effective for models with finite state and action space. This paper establishes ...

Nowadays, the intelligent transportation concept has become one of the most important research fields. All of us depend on mobility, even when we talk about people, provide services, or move goods. Researchers have tried to create and test different transportation models that can optimize traffic flow through road networks and, implicitly, reduce travel times. To validate these new models, the necessity of having a calibration process defined has emerged. Calibration is mandatory in the modeling process because it ensures the achievement of a model closer to the real system. The purpose of this paper is to propose a new multidisciplinary approach combining microscopic traffic modeling theory with intelligent control systems concepts like fuzzy inference in the traffic model calibration. The chosen Takagi-Sugeno fuzzy inference system proves its adaptive capacity for real-time systems. This concept will be applied to the specific microscopic car-following model parameters in combination with a Kalman filter. The results will demonstrate how the microscopic traffic model parameters can adapt based on real data to prove the model validity.

Studying the time-related course of psychological processes is a challenging endeavor, particularly over long developmental periods. Accelerated longitudinal designs (ALD) allow capturing such periods with a limited number of assessments in a much shorter time framework. In ALDs, participants from different cohorts are measured repeatedly but the measures provided by each participant cover only a fraction of the time range of the study. It is then assumed that the common trajectory can be studied by aggregating the information provided by the different converging cohorts. We conducted a Monte Carlo study to evaluate the practical relevance of using discrete- and continuous-time latent change score models for recovering the trajectories of a developmental process from ALD data under different sampling conditions. We focused on exponential trajectories typically found in the development of cognitive abilities from childhood to early adulthood. The results support the appropriateness of ALD designs to study such processes under various conditions of sampling. When all cohorts are drawn from the same population, both discrete- and continuous-time models are able to recover the parameters defining the underlying developmental process. However, discrete-time models yield biased estimates when time lags between observations are not constant. When cohorts are not from the same population and, thus, lack convergence, both types of models show bias in various parameters. We discuss the findings in the context of developmental methodology, encourage researchers to adopt continuous time models to analyze data from ALDs, and provide recommendations about how to implement such research designs.

There has been significant progress in the area of short-term scheduling of batch processes, including the solution of industrial-sized problems, in the last 20 years. The main goal of this paper is to provide an up-to-date review of the state-of-the-art in this challenging area. Main features, strengths and limitations of existing modeling and optimization techniques as well as other available major solution methods are examined through this paper. We first present a general classification for scheduling problems of batch processes as well as for the corresponding optimization models. Subsequently, the modeling of representative optimization approaches for the different problem types are introduced in detail, focusing on both discrete and continuous time models. A comparison of effectiveness and efficiency of these models is given for two benchmarking examples from the literature. We also discuss two real-world applications of scheduling problems that cannot be readily accommodated using existing methods. For the sake of completeness, other alternative solution methods applied in the field of scheduling are also reviewed, followed by a discussion related to solving large-scale problems through rigorous optimization approaches. Finally, we list available academic and commercial software, and briefly address the issue of rescheduling capabilities of the various optimization approaches as well as important extensions that go beyond short-term batch scheduling.

An instrumental variable method for continuous-time model identification is proposed for multiple input single output systems where the characteristic polynomials of the transfer functions associated with each input are not constrained to be identical. An associated model order determination procedure is shown to be reasonably successful. Monte Carlo simulation analyses are used to demonstrate the properties and general robustness of the model order selection and parameter estimation schemes. The results obtained to model a winding process and an industrial binary distillation column illustrate the practical applicability of the proposed identification scheme.

... Gk'(s) = Tak ST-l'%t&) ; yk=l, G ,ts)= Tak(sT+l-log(d ; ykz2 k (ST-lOid& ))' ' (6) ... communications, Vol. 33, pp. 249-258, March 1985. Omid Shoaei, Continuous-Time Delta-Sigma A/D Converters for High Speed Applications, Ph.D. dissertation, Carleton University, November 1995. ...

Considerable literature now exists on stochastic models for the reproductive history of a cohort of couples. These models are of varying complexity and the relationships between separate treatments are not always clear. A classification system for such models is proposed, followed by a historical review of models for family building and for logically related processes. Models, differing only in treatment

This dissertation focuses on the construction of macroeconomic models that can be used to evaluate monetary policy. The theoretical models developed for this purpose emphasize the importance of intertemporal optimizing behaviour, the role of expectations and nominal price ...

This Working Paper should not be reported as representing the views of the IMF. The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate. We explore the role of business services in knowledge accumulation and growth and the determinants of knowledge diffusion including the role of distance. A continuous-time model is estimated on several European countries, Japan, and the United States. Policy simulations illustrate the benefits for EU growth of the deepening of the single market, the reduction of regulatory barriers, and the accumulation of technology and human capital. Our results support the basic insights of the Lisbon Agenda. Economic growth in Europe is enhanced to the extent that: trade in services increases, technology accumulation and diffusion increase, regulation becomes both l...

This paper presents continuous time models for an analysis of dynamic systems using them to examine the complex dynamics of collective action and political change. The study concentrates on the mutual dependence and behavior of two variables over time: the number of citizens participating in collective action, and the amount of resources mobilized by the government to combat such collective

This paper first gives a tutorial introduction to the main aspects of existing time-domain methods and software for identifying linear continuous-time models of dynamical systems from sampled input/output data. The second part of the paper demonstrates these approaches via simulated and real data examples.