Spelling suggestions: "subject:"stochastic analysis"" "subject:"ctochastic analysis""
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Rational Hedging and Valuation with Utility-Based PreferencesLuedenscheid 29 October 2001 (has links) (PDF)
No description available.
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How well can one resolve the state space of a chaotic map?Lippolis, Domenico 06 April 2010 (has links)
All physical systems are affected by some noise that limits the resolution that can be attained in partitioning their state space. For chaotic, locally hyperbolic flows, this resolution depends on the interplay of the local stretching/contraction and the smearing due to noise. My goal is to determine the `finest attainable' partition for a given hyperbolic dynamical system and a given weak additive
white noise. That is achieved by computing the local eigenfunctions of the Fokker-Planck evolution operator in linearized neighborhoods of the periodic orbits of the corresponding deterministic system, and using overlaps of
their widths as the criterion for an optimal partition. The Fokker-Planck evolution is then represented by a finite transition graph, whose spectral determinant yields time averages of dynamical observables. The method applies in
principle to both continuous- and discrete-time dynamical systems. Numerical tests of such optimal partitions on unimodal maps support my hypothesis.
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Scaling limit for the diffusion exit problemAlmada Monter, Sergio Angel 01 April 2011 (has links)
A stochastic differential equation with vanishing martingale term is studied. Specifically, given a domain D, the asymptotic scaling properties of both the exit time from the domain and the exit distribution are considered under the additional (non-standard) hypothesis that the initial condition also has a scaling limit. Methods from dynamical systems are applied to get more complete estimates than the ones obtained by the probabilistic large deviation theory.
Two situations are completely analyzed. When there is a unique critical saddle point of the deterministic system (the system without random effects), and when the unperturbed system escapes the domain D in finite time. Applications to these results are in order. In particular, the study of 2-dimensional heteroclinic networks is closed with these results and shows the existence of possible asymmetries. Also, 1-dimensional diffusions conditioned to rare events are further studied using these results as building blocks.
The approach tries to mimic the well known linear situation. The original equation is smoothly transformed into a very specific non-linear equation that is treated as a singular perturbation of the original equation. The transformation provides a classification to all 2-dimensional systems with initial conditions close to a saddle point of the flow generated by the drift vector field. The proof then proceeds by estimates that propagate the small noise nature of the system through the non-linearity. Some proofs are based on geometrical arguments and stochastic pathwise expansions in noise intensity series.
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The use of absorbing boundaries in the analysis of bankruptcyHildebrand, Paul 11 1900 (has links)
An explicit solution is given for the value of a risk neutral firm with stochastic revenue facing the
possibility of bankruptcy. The analysis is conducted in continuous time. Uncertainty is modeled
using an Ito process and bankruptcy is modeled as an absorbing boundary. The analysis yields
an ordinary differential equation with a closed form solution. The value function is used to
calculate the firm's demand for high interest rate loans, showing a positive demand at interest
rates which appear intuitively to be excessive. A value function is also derived for a risk neutral
lender advancing funds to the firm. The borrowing and lending value functions are then used to
examine various aspects of lender-borrower transactions under different bargaining structures. In
a competitive lending market, the model shows that credit rationing occurs inevitably. In a
monopoly lending market, the lender sets interest rates and maximum loan levels which reduce
the borrower to zero profit. When a second borrower is introduced, the lender must allocate
limited funds between two borrowers. A lender is shown to squeeze the smaller "riskier"
borrower out of the market when the lender's overall credit constraint is tight. Under each
bargaining structure, the model is also used to examine changes in the respective "salvage"
recoveries of the lender and borrower on bankruptcy.
Accepted:
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Analysis of a simple gene expression modelChipindirwi, Simbarashe January 2012 (has links)
Gene expression is random owing to the low copy numbers of molecules in a living cell
and the best way to study it is by use of a stochastic method, specifically the chemical
master equation. The method is used here to derive analytically the invariant probability
distributions, and expressions for the moments and noise strength for a simple gene model
without feedback. Sensitivity analysis, emphasizing particularly the dependence of the
probability distributions, the moments, and noise strength is carried out using Metabolic
Control Analysis, which uses control coefficients that measure the response of observables
when parameters change. Bifurcation analysis is also carried out. The results show that the
number of mRNA molecules follows a hypergeometric probability distribution, and that
noise decreases as the number of these molecules increases. Metabolic Control Analysis
was successfully extended to genetic control mechanisms, with the obtained control coefficients
satisfying a summation theorem. The system undergoes stochastic bifurcations as
parameters change. / xii, 86 leaves : ill. ; 29 cm
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Numerical analysis of the nonlinear dynamics of a drill-string with uncertainty modelingRitto, Thiago 07 April 2010 (has links) (PDF)
This thesis analyzes the nonlinear dynamics of a drill-string including uncertainty modeling. A drill-string is a slender flexible structure that rotates and digs into the rock in search of oil. A mathematical-mechanical model is developed for this structure including fluid-structure interaction, impact, geometrical nonlinearities and bit-rock interaction. After the derivation of the equations of motion, the system is discretized by means of the finite element method and a computer code is developed for the numerical computations using the software MATLAB. The normal modes of the dynamical system in the prestressed configuration are used to construct a reduced order model for the system. To take into account uncertainties, the nonparametric probabilistic approach, which is able to take into account both system-parameter and model uncertainties, is used. The probability density functions related to the random variables are constructed using the maximum entropy principle and the stochastic response of the system is calculated using the Monte Carlo method. A novel approach to take into account model uncertainties in a nonlinear constitutive equation (bit-rock interaction model) is developed using the nonparametric probabilistic approach. To identify the probabilistic model of the bit-rock interaction model, the maximum likelihood method together with a statistical reduction in the frequency domain (using the Principal Component Analysis) is applied. Finally, a robust optimization problem is performed to find the operational parameters of the system that maximizes its performance, respecting the integrity limits of the system, such as fatigue and instability
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Screening for breast cancer : an assessment of various stochastic modelsJoseph, Lawrence, 1959- January 1984 (has links)
No description available.
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Radiobiological modeling using track structure analysisCoghill, Matthew Taylor 21 May 2012 (has links)
The purpose of this thesis is to present data pertinent to and propose conclusions regarding the coordination
of radiobiologic effectiveness (RBE) and linear energy transfer (LET). RBE is a quantity relating the effectiveness
of different radiations in causing cell death. LET is a measure of the rate of energy transferred to material by an
ionizing particle. This relationship of these values varies for different particles. The reason for this is still inconclusive. The petitioner has made use of a toolkit for Geant4, known as Geant4-DNA, to perform track-structure analysis on a chromosome model. Geant4 is an object-oriented program for the "simulation of the passage of particles through matter" developed by CERN that makes use of Monte Carlo methods and is expanded by Geant4-DNA to handle low-energy electron physics as well as physic-chemical effects. The chromosome model, in this case, has been developed by the petitioner as a nucleus with a basic, uniform distribution of chromatin. Radiation damage to DNA, in the form of aberrations, lesions and strand breaks, can be coordinated to energy deposited or number of ionizations occurring in the target (in this case DNA or chromatin fiber). Certain threshold values have been established as indicate of different types of DNA damage. The ultimate goal of this work is to score these clusters of events against the threshold values to determine the severity of DNA damage. The final comparison of the results for different particles will provide for a better understanding of the RBE-LET relationships by improving the understanding of the underlying nanodosimetric qualities.
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Optimization based methods for solving some problems in telecommunications and the internetJia, Long January 2005 (has links)
The purpose of this thesis is to develop some new algorithms based on optimization techniques for solving some problems in some areas of telecommunications and the Internet. There are two main parts to this thesis. In the first part we discuss optimization based stochastic and queueing models in telecommunications network corrective maintenance. In the second part we develop optimization based clustering (OBC) algorithms for network evolution and multicast routing. The most typical scenario encountered during mathematical optimization modelling in telecommunications, for example, is to minimize the cost of establishment and maintenance of the networks subject to the performance constraints of the networks and the reliability constraints of the networks as well. Most of these optimization problems are global optimization, that is, they have many local minima and most of these local minima do not provide any useful information for solving these problems. Therefore, the development of effective methods for solving such global optimization problems is important. To run the telecommunications networks with cost-effective network maintenance,we need to establish a practical maintenance model and optimize it. In the first part of the thesis, we solve a known stochastic programming maintenance optimization model with a direct method and then develop some new models. After that we introduce queue programming models in telecommunications network maintenance optimization. The ideas of profit, loss, and penalty will help telecommunications companies have a good view of their maintenance policies and help them improve their service. In the second part of this thesis we propose the use of optimization based clustering (OBC) algorithms to determine level-constrained hierarchical trees for network evolution and multicast routing. This problem is formulated as an optimization problem with a non-smooth, non-convex objective function. Different algorithms are examined for solving this problem. Results of numerical experiments using some artifiicial and real-world databases are reported. / Doctor of Philosophy
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Optimization based methods for solving some problems in telecommunications and the internetJia, Long . University of Ballarat. January 2005 (has links)
The purpose of this thesis is to develop some new algorithms based on optimization techniques for solving some problems in some areas of telecommunications and the Internet. There are two main parts to this thesis. In the first part we discuss optimization based stochastic and queueing models in telecommunications network corrective maintenance. In the second part we develop optimization based clustering (OBC) algorithms for network evolution and multicast routing. The most typical scenario encountered during mathematical optimization modelling in telecommunications, for example, is to minimize the cost of establishment and maintenance of the networks subject to the performance constraints of the networks and the reliability constraints of the networks as well. Most of these optimization problems are global optimization, that is, they have many local minima and most of these local minima do not provide any useful information for solving these problems. Therefore, the development of effective methods for solving such global optimization problems is important. To run the telecommunications networks with cost-effective network maintenance,we need to establish a practical maintenance model and optimize it. In the first part of the thesis, we solve a known stochastic programming maintenance optimization model with a direct method and then develop some new models. After that we introduce queue programming models in telecommunications network maintenance optimization. The ideas of profit, loss, and penalty will help telecommunications companies have a good view of their maintenance policies and help them improve their service. In the second part of this thesis we propose the use of optimization based clustering (OBC) algorithms to determine level-constrained hierarchical trees for network evolution and multicast routing. This problem is formulated as an optimization problem with a non-smooth, non-convex objective function. Different algorithms are examined for solving this problem. Results of numerical experiments using some artifiicial and real-world databases are reported. / Doctor of Philosophy
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