Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

The Transmission of Monetary Policy in a Multi-Sector Economy

This paper constructs and estimates a sticky-price, Dynamic Stochastic General Equilibrium model with heterogenous production sectors. Sectors differ in price stickiness, capital-adjustment costs and production technology, and use output from each other as material and investment inputs following an Input-Output Matrix and Capital Flow Table that represent the U.S. economy. By relaxing the standard assumption of symmetry, this model allows different sectoral dynamics in response to monetary policy shocks. The model is estimated by Simulated Method of Moments using sectoral and aggregate U.S. time series. Results indicate 1) substantial heterogeneity in price stickiness across sectors, with quantitatively larger differences between services and goods than previously found in micro studies that focus on final goods alone, 2) a strong sensitivity to monetary policy shocks on the part of construction and durable manufacturing, and 3) similar quantitative predictions at the aggregate level by the multi-sector model and a standard model that assumes symmetry across sectors.

Dissent in monetary policy decisions

Voting records indicate that dissents in monetary policy committees are frequent and predictability regressions show that they help forecast future policy decisions. In order to study whether the latter relation is causal, we construct a model of committee decision making and dissent where members' decisions are not a function of past dissents. The model is estimated using voting data from the Bank of England and the Riksbank. Stochastic simulations show that the decision-making frictions in our model help account for the predictive power of current dissents. The effect of insti- tutional characteristics and structural parameters on dissent rates is examined using simulations as well.

Analysis of Some Stochastic Inventory Models with Pooling Retrial of Customers

The thesis deals with analysis of some Stochastic Inventory Models with Pooling/Retrial of Customers.. In the first model we analyze an (s,S) production Inventory system with retrial of customers. Arrival of customers from outside the system form a Poisson process. The inter production times are exponentially distributed with parameter µ. When inventory level reaches zero further arriving demands are sent to the orbit which has capacity M(<∞). Customers, who find the orbit full and inventory level at zero are lost to the system. Demands arising from the orbital customers are exponentially distributed with parameter γ. In the model-II we extend these results to perishable inventory system assuming that the life-time of each item follows exponential with parameter θ. The study deals with an (s,S) production inventory with service times and retrial of unsatisfied customers. Primary demands occur according to a Markovian Arrival Process(MAP). Consider an (s,S)-retrial inventory with service time in which primary demands occur according to a Batch Markovian Arrival Process (BMAP). The inventory is controlled by the (s,S) policy and (s,S) inventory system with service time. Primary demands occur according to Poissson process with parameter λ. The study concentrates two models. In the first model we analyze an (s,S) Inventory system with postponed demands where arrivals of demands form a Poisson process. In the second model, we extend our results to perishable inventory system assuming that the life-time of each item follows exponential distribution with parameter θ. Also it is assumed that when inventory level is zero the arriving demands choose to enter the pool with probability β and with complementary probability (1- β) it is lost for ever. Finally it analyze an (s,S) production inventory system with switching time. A lot of work is reported under the assumption that the switching time is negligible but this is not the case for several real life situation.

Stochastic Modelling Using Markov Chains

Department of Statistics, Cochin University of Science and Technology

Wage policy in Indian industries

India is on the threshold of industrial and economic development. The growth would be retarded if harmonious employer-employee relations are not maintained. 'Wages' plays a fundamental role in establishing this relationship. However, much controversy in the industrial sphere revolves round the question of wages. Though formerly the laissez faire doctrine prevailed, with the emergence of the welfare state ideology, notions of national economy and social justice gained prominence. The problem of wages has became one with social, political, economic, psychological and legal dimensions. Formulation of a proper wage policy is thus a riddle. Realities of the present have to be fused with perspectives about the future. With due recognition of all significant factors, a proper balance has to be struck, which should be the hard core of any wage policy. This study emphasises the need for a wage policy which may meet the requirements of rapid economic growth and stable industrial relations. The study also indicates the proper bases for the promotien of such a policy.

Studies on Inventory with Positive Service Time Under Local Purchase Driven by N/T- Policy

In this thesis, certain continuous time inventory problems with positive service time under local purchase guided by N/T-policy are analysed. In most of the cases analysed, we arrive at stochastic decomposition of system states, that is, the joint distribution of the system states is obtained as the product of marginal distributions of the components. The thesis is divided into ve chapters

Dual technological development in Botswana agriculture: A Stochastic input distance function approach

To improve the welfare of the rural poor and keep them in the countryside, the government of Botswana has been spending 40% of the value of agricultural GDP on agricultural support services. But can investment make smallholder agriculture prosperous in such adverse conditions? This paper derives an answer by applying a two-output six-input stochastic translog distance function, with inefficiency effects and biased technical change to panel data for the 18 districts and the commercial agricultural sector, from 1979 to 1996 This model demonstrates that herds are the most important input, followed by draft power. land and seeds. Multilateral indices for technical change, technical efficiency and total factor productivity (TFP) show that the technology level of the commercial agricultural sector is more than six times that of traditional agriculture and that the gap has been increasing, due to technological regression in traditional agriculture and modest progress in commercial agriculture. Since the levels of efficiency are similar, the same patient is repeated by the TFP indices. This result highlights the policy dilemma of the trade-off between efficiency and equity objectives.

Minimum stable convergence criteria for stochastic diffusion search

An analysis of Stochastic Diffusion Search (SDS), a novel and efficient optimisation and search algorithm, is presented, resulting in a derivation of the minimum acceptable match resulting in a stable convergence within a noisy search space. The applicability of SDS can therefore be assessed for a given problem.

Fit for policy? Some evidence on the application of development viability models in the UK planning system

This paper investigates the application and use of development viability models in the formation of planning policies in the UK. Particular attention is paid to three key areas; the assumed development scheme in development viability models, the use of forecasts and the debate concerning Threshold Land Value. The empirical section reports on the results of an interview survey involving the main producers of development viability models and appraisals. It is concluded that, although development viability models have intrinsic limitations associated with model composition and input uncertainties, the most significant limitations are related to the ways that they have been adapted for use in the planning system. In addition, it is suggested that the contested nature of Threshold Land Value is an example of calculative practices providing a façade of technocratic rationality in the planning system.

Area-wide development viability appraisals: the concept of threshold land value within a UK planning context

Area-wide development viability appraisals are undertaken to determine the economic feasibility of policy targets in relation to planning obligations. Essentially, development viability appraisals consist of a series of residual valuations of hypothetical development sites across a local authority area at a particular point in time. The valuations incorporate the estimated financial implications of the proposed level of planning obligations. To determine viability the output land values are benchmarked against threshold land value and therefore the basis on which this threshold is established and the level at which it is set is critical to development viability appraisal at the policy-setting (area-wide) level. Essentially it is an estimate of the value at which a landowner would be prepared to sell. If the estimated site values are higher than the threshold land value the policy target is considered viable. This paper investigates the effectiveness of existing methods of determining threshold land value. They will be tested against the relationship between development value and costs. Modelling reveals that threshold land value that is not related to shifts in development value renders marginal sites unviable and fails to collect proportionate planning obligations from high value/low cost sites. Testing the model against national average house prices and build costs reveals the high degree of volatility in residual land values over time and underlines the importance of making threshold land value relative to the main driver of this volatility, namely development value.

The significance of occupancy steadiness in residential consumer response to Time of Use pricing: Evidence from a stochastic adjustment model

The recent roll-out of smart metering technologies in several developed countries has intensified research on the impacts of Time-of-Use (TOU) pricing on consumption. This paper analyses a TOU dataset from the Province of Trento in Northern Italy using a stochastic adjustment model. Findings highlight the non-steadiness of the relationship between consumption and TOU price. Weather and active occupancy can partly explain future consumption in relation to price.

The real-time optimisation of DNO owned storage devices on the LV network for peak reduction

Energy storage is a potential alternative to conventional network reinforcementof the low voltage (LV) distribution network to ensure the grid’s infrastructure remainswithin its operating constraints. This paper presents a study on the control of such storagedevices, owned by distribution network operators. A deterministic model predictive control (MPC) controller and a stochastic receding horizon controller (SRHC) are presented, wherethe objective is to achieve the greatest peak reduction in demand, for a given storagedevice specification, taking into account the high level of uncertainty in the prediction of LV demand. The algorithms presented in this paper are compared to a standard set-pointcontroller and bench marked against a control algorithm with a perfect forecast. A specificcase study, using storage on the LV network, is presented, and the results of each algorithmare compared. A comprehensive analysis is then carried out simulating a large number of LV networks of varying numbers of households. The results show that the performance of each algorithm is dependent on the number of aggregated households. However, on a typical aggregation, the novel SRHC algorithm presented in this paper is shown to outperform each of the comparable storage control techniques.

Correlation times in stochastic equations with delayed feedback and multiplicative noise

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Mathematical optimisation techniques applied to power system operation and planning

Nowadays, power system operation becomes more complex because of the critical operating conditions resulting from the requirements of a market-driven operation. In this context, efficient methods for optimisation of power system operation and planning become critical to satisfy the operational (technical), financial and economic demands. Therefore, the detailed analysis of modern optimisation techniques as well as their application to the power system problems represent a relevant issue from the scientific and technological points of view. This paper presents a brief overview of the developments on modern mathematical optimisation methods applied to power system operation and planning. Copyright © 2007 Inderscience Enterprises Ltd.