Analysis of Some Stochastic Inventory Models with Pooling/ Retrial of Customers

In this thesis we have presented several inventory models of utility. Of these inventory with retrial of unsatisfied demands and inventory with postponed work are quite recently introduced concepts, the latt~~ being introduced for the first time. Inventory with service time is relatively new with a handful of research work reported. The di lficuity encoLlntered in inventory with service, unlike the queueing process, is that even the simplest case needs a 2-dimensional process for its description. Only in certain specific cases we can introduce generating function • to solve for the system state distribution. However numerical procedures can be developed for solving these problem.

The role of lower partial moments in stochastic modeling

Lower partial moments plays an important role in the analysis of risks and in income/poverty studies. In the present paper, we further investigate its importance in stochastic modeling and prove some characterization theorems arising out of it. We also identify its relationships with other important applied models such as weighted and equilibrium models. Finally, some applications of lower partial moments in poverty studies are also examined

Analysis of Stochastic Volatility Sequences Generated by Product Autoregressive Models

The classical methods of analysing time series by Box-Jenkins approach assume that the observed series uctuates around changing levels with constant variance. That is, the time series is assumed to be of homoscedastic nature. However, the nancial time series exhibits the presence of heteroscedasticity in the sense that, it possesses non-constant conditional variance given the past observations. So, the analysis of nancial time series, requires the modelling of such variances, which may depend on some time dependent factors or its own past values. This lead to introduction of several classes of models to study the behaviour of nancial time series. See Taylor (1986), Tsay (2005), Rachev et al. (2007). The class of models, used to describe the evolution of conditional variances is referred to as stochastic volatility modelsThe stochastic models available to analyse the conditional variances, are based on either normal or log-normal distributions. One of the objectives of the present study is to explore the possibility of employing some non-Gaussian distributions to model the volatility sequences and then study the behaviour of the resulting return series. This lead us to work on the related problem of statistical inference, which is the main contribution of the thesis

On the Convergence of Stochastic Iterative Dynamic Programming Algorithms

Recent developments in the area of reinforcement learning have yielded a number of new algorithms for the prediction and control of Markovian environments. These algorithms, including the TD(lambda) algorithm of Sutton (1988) and the Q-learning algorithm of Watkins (1989), can be motivated heuristically as approximations to dynamic programming (DP). In this paper we provide a rigorous proof of convergence of these DP-based learning algorithms by relating them to the powerful techniques of stochastic approximation theory via a new convergence theorem. The theorem establishes a general class of convergent algorithms to which both TD(lambda) and Q-learning belong.

Stochastic Processes

Exercises, exams and solutions for a second year maths course.

Dynamic programming for stochastic target problems, Viscosity solutions and hedging in markets with Portfolio constraints and large investors

The purpose of this expository arti le is to present a self- ontained overview of some results on the hara terization of the optimal value fun tion of a sto hasti target problem as (dis ontinuous) vis osity solution of a ertain dynami programming PDE and its appli ation to the problem of hedging ontingent laims in the presen e of portfolio onstraints and large investors

Distinct Unfolding and Refolding Pathways of Ribonuclease A Revealed by Heating and Cooling Temperature Jumps

Heating and cooling temperature jumps (T-jumps) were performed using a newly developed technique to trigger unfolding and refolding of wild-type ribonuclease A and a tryptophan-containing variant (Y115W). From the linear Arrhenius plots of the microscopic folding and unfolding rate constants, activation enthalpy (ΔH#), and activation entropy (ΔS#) were determined to characterize the kinetic transition states (TS) for the unfolding and refolding reactions. The single TS of the wild-type protein was split into three for the Y115W variant. Two of these transition states, TS1 and TS2, characterize a slow kinetic phase, and one, TS3, a fast phase. Heating T-jumps induced protein unfolding via TS2 and TS3; cooling T-jumps induced refolding via TS1 and TS3. The observed speed of the fast phase increased at lower temperature, due to a strongly negative ΔH# of the folding-rate constant. The results are consistent with a path-dependent protein folding/unfolding mechanism. TS1 and TS2 are likely to reflect X-Pro114 isomerization in the folded and unfolded protein, respectively, and TS3 the local conformational change of the β-hairpin comprising Trp115. A very fast protein folding/unfolding phase appears to precede both processes. The path dependence of the observed kinetics is suggestive of a rugged energy protein folding funne

A Filter for Visual Tracking Based on a Stochastic Model for Driver Behaviour

A driver controls a car by turning the steering wheel or by pressing on the accelerator or the brake. These actions are modelled by Gaussian processes, leading to a stochastic model for the motion of the car. The stochastic model is the basis of a new filter for tracking and predicting the motion of the car, using measurements obtained by fitting a rigid 3D model to a monocular sequence of video images. Experiments show that the filter easily outperforms traditional filters.

Climate response to basin-scale warming and cooling of the North Atlantic Ocean

Using experiments with an atmospheric general circulation model, the climate impacts of a basin-scale warming or cooling of the North Atlantic Ocean are investigated. Multidecadal fluctuations with this pattern were observed during the twentieth century, and similar variations--but with larger amplitude--are believed to have occurred in the more distant past. It is found that in all seasons the response to warming the North Atlantic is strongest, in the sense of highest signal-to-noise ratio, in the Tropics. However there is a large seasonal cycle in the climate impacts. The strongest response is found in boreal summer and is associated with suppressed precipitation and elevated temperatures over the lower-latitude parts of North and South America. In August­-September-­October there is a significant reduction in the vertical shear in the main development region for Atlantic hurricanes. In winter and spring, temperature anomalies over land in the extratropics are governed by dynamical changes in circulation rather than simply reflecting a thermodynamic response to the warming or cooling of the ocean. The tropical climate response is primarily forced by the tropical SST anomalies, and the major features are in line with simple models of the tropical circulation response to diabatic heating anomalies. The extratropical climate response is influenced both by tropical and higher-latitude SST anomalies and exhibits nonlinear sensitivity to the sign of the SST forcing. Comparisons with multidecadal changes in sea level pressure observed in the twentieth century support the conclusion that the impact of North Atlantic SST change is most important in summer, but also suggest a significant influence in lower latitudes in autumn and winter. Significant climate impacts are not restricted to the Atlantic basin, implying that the Atlantic Ocean could be an important driver of global decadal variability. The strongest remote impacts are found to occur in the tropical Pacific region in June­-August and September­-November. Surface anomalies in this region have the potential to excite coupled ocean­atmosphere feedbacks, which are likely to play an important role in shaping the ultimate climate response.

Stochastic modelling of rainfall from satellite data

Satellite-based rainfall monitoring is widely used for climatological studies because of its full global coverage but it is also of great importance for operational purposes especially in areas such as Africa where there is a lack of ground-based rainfall data. Satellite rainfall estimates have enormous potential benefits as input to hydrological and agricultural models because of their real time availability, low cost and full spatial coverage. One issue that needs to be addressed is the uncertainty on these estimates. This is particularly important in assessing the likely errors on the output from non-linear models (rainfall-runoff or crop yield) which make use of the rainfall estimates, aggregated over an area, as input. Correct assessment of the uncertainty on the rainfall is non-trivial as it must take account of • the difference in spatial support of the satellite information and independent data used for calibration • uncertainties on the independent calibration data • the non-Gaussian distribution of rainfall amount • the spatial intermittency of rainfall • the spatial correlation of the rainfall field This paper describes a method for estimating the uncertainty on satellite-based rainfall values taking account of these factors. The method involves firstly a stochastic calibration which completely describes the probability of rainfall occurrence and the pdf of rainfall amount for a given satellite value, and secondly the generation of ensemble of rainfall fields based on the stochastic calibration but with the correct spatial correlation structure within each ensemble member. This is achieved by the use of geostatistical sequential simulation. The ensemble generated in this way may be used to estimate uncertainty at larger spatial scales. A case study of daily rainfall monitoring in the Gambia, west Africa for the purpose of crop yield forecasting is presented to illustrate the method.

Comparison of stochastic parametrization approaches in a single-column model

We discuss and test the potential usefulness of single-column models (SCMs) for the testing of stchastic physics schemes that have been proposed for use in general circulation models (GCMs). We argue that although single column tests cannot be definitive in exposing the full behaviour of a stochastic method in the full GCM, and although there are differences between SCM testing of deterministic and stochastic methods, nonetheless SCM testing remains a useful tool. It is necessary to consider an ensemble of SCM runs produced by the stochastic method. These can be usefully compared to deterministic ensembles describing initial condition uncertainty and also to combinations of these (with structural model changes) into poor man's ensembles. The proposed methodology is demonstrated using an SCM experiment recently developed by the GCSS community, simulating the transitions between active and suppressed periods of tropical convection.

A stochastic parameterization for deep convection based on equilibrium statistics

A stochastic parameterization scheme for deep convection is described, suitable for use in both climate and NWP models. Theoretical arguments and the results of cloud-resolving models, are discussed in order to motivate the form of the scheme. In the deterministic limit, it tends to a spectrum of entraining/detraining plumes and is similar to other current parameterizations. The stochastic variability describes the local fluctuations about a large-scale equilibrium state. Plumes are drawn at random from a probability distribution function (pdf) that defines the chance of finding a plume of given cloud-base mass flux within each model grid box. The normalization of the pdf is given by the ensemble-mean mass flux, and this is computed with a CAPE closure method. The characteristics of each plume produced are determined using an adaptation of the plume model from the Kain-Fritsch parameterization. Initial tests in the single column version of the Unified Model verify that the scheme is effective in producing the desired distributions of convective variability without adversely affecting the mean state.