Lin Jianzhong. / "May 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 106-118). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

The purpose of this thesis is to determine the most effective parallel algorithm for the solution of the parabolic differential equations characteristic of diffusion problems. The primary aim is to apply the chosen algorithm to obtain solutions to the equations governing the operation of membrane-covered oxygen sensors, known as Clark electrodes, which are used for monitoring the oxygen concentration of blood. The boundary conditions of this problem require the development of a singularity correction technique. A brief history of electrochemical sensors leading to the development of the Clark electrode is given, together with the two-dimensional equations and boundary conditions governing its operation. A locally valid series expansion is derived to take care of the boundary singularity, together with a robust method of matching this to the finite difference approximation. Parallel implementations of three representative numerical algorithms applied to a simple model problem are compared by extending Leland's parallel effectiveness model. The chosen parallel algorithm is combined with the singularity correction to obtain a solution to the Clark electrode problem. Numerical experiments show this solution to achieve the required accuracy. Previous one-dimensional models of the Clark electrode are shown to be inadequate before the two-dimensional model is used to examine the variation of operation with design. The understanding gained allows us to demonstrate the advantages of pulse amperometry over steady-state techniques, and to suggest the most appropriate method and design for use in in vivo clinical monitoring.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Wendell H. Fleming, Sanjoy K. Mitter. / "January 1982" "September 9, 1981" "DOE/ET-76-A-012295" / "AF-AFOSR 76-3063D" "MCS-79-03554"

No description available.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Diffusion processes play an important role in describing systems in many fields of science, as in physics, biology, finance and social science. One of the most famous examples of the diffusion process is the Brownian motion.    At mesoscopic scale, the Brownian theory describes the very irregular and animated motion of a particle suspended in a fluid. In this thesis, the dynamics and thermodynamics of diffusion processes driven out of equilibrium, at mesoscopic scale, are investigated.    For dynamics, the theory of Brownian motion for a particle which is able to rotate and translate in three dimensions is presented.  Moreover, it is presented how to treat diffusion process on n-dimensional Riemann manifolds defining the Kolmogorov forward equation on such manifold.   For thermodynamics, this thesis describes how to define thermodynamics quantities at mesoscopic scale using the tools of Brownian theory. The theory of stochastic energetics and how to compute entropy production along a trajectory are presented introducing the new field of stochastic thermodynamics. Moreover, the "anomalous entropy production" is introduced. This anomaly in the entropy production arises when diffusion processes are driven out of equilibrium by space dependent temperature field. The presence of this term expresses the fallacy of the overdamped approximation in computing thermodynamic quantities.    In the first part of the thesis the translational and rotational motion of an ellipsoidal particle in a heterogeneous thermal environment, with a space-dependent temperature field, is analyzed from the point of view of stochastic thermodynamics.    In the final part of the thesis, the motion of a Brownian rigid body three-dimensional space in a homogeneous thermal environment under the presence of an external force field is analyzed, using multiscale method and homogenization. / <p>QC 20170515</p>

Diffusion processes provide a natural way of modelling a variety of physical and economic phenomena. It is often the case that one is unable to observe a diffusion process directly, and must instead rely on noisy observations that are discretely spaced in time. Given these discrete, noisy observations, one is faced with the task of inferring properties of the underlying diffusion process. For example, one might be interested in inferring the current state of the process given observations up to the present time (this is known as the filtering problem). Alternatively, one might wish to infer parameters governing the time evolution the diffusion process. In general, one cannot apply Bayes’ theorem directly, since the transition density of a general nonlinear diffusion is not computationally tractable. In this thesis, we investigate a novel method of simplifying the problem. The stochastic differential equation that describes the diffusion process is replaced with a simpler ordinary differential equation, which has a random driving noise that approximates Brownian motion. We show how one can exploit this approximation to improve on standard methods for inferring properties of nonlinear diffusion processes.

随着全球金融市场的日益创新和不断加剧的竞争，金融产品也变得越来越结构复杂。这些复杂的金融产品，从定价，对冲到风险管理，都对相应的数学技术提出越来越高的要求。在目前运用的技术中，蒙特卡洛模拟方法由于其广泛的适用性而备受欢迎。本篇论文对于在金融工程和工业界都受到广泛关注的两个问题进行研究：局部化以及对于受布朗运动驱动的随机微分方程的精确抽样；布朗河曲，重要性抽样已经对于扩散过程极值的无偏估计。 / 第一篇文章考虑了使用蒙特卡洛模拟方法产生随机微分方程的样本路径。离散化方法是此前普遍使用的近似产生路径的方法：这种方法很容易实施，但是会产生抽样偏差。本篇文章提出一种模拟方法，可用于随机微分方程路径的精确抽样。一个至关重要的发现是：随机微分方程的概率分布可以被分解为两部分的乘积，一部分是标准布朗运动的概率分布，另外一部分是双重随机的泊松过程。基于这样的分解和局部化技术，本篇文章提出一种接受-拒绝算法。数值试验可以验证，这种方法的均方误差-计算时间的收敛速度可以达到O(t⁻¹[superscript /]²)，优于传统的离散化方法。更进一步的优点是：这种方法可以对带边界的随机微分方程进行精确抽样，而带边界的微分方程正是传统离散方法经常遇到困难的情形。 / 第二篇文章研究了如何计算基于扩散过程极值的泛函。传统的离散化方法收率速度很慢。本篇文章提出了一种基于维纳测度分解的无偏蒙特卡洛估计。运用重要性抽样技术和对于布朗运动路径的威廉分解，本篇文章将对于一般性扩散过程的极值的抽样化简为对于两个布朗河曲的抽样。数值试验部分也验证了本篇文章所提方法的准确性和计算上的高效率。 / With increased innovation and competition in the current financial market, financial product has become more and more complicated, which requires advanced techniques in pricing, hedging and risk management. Monte Carlo simulation is among the most popular ones due to its great °exibility. This dissertation contains two problems recently arises and receives much attention from both the financial engineering and simulation communities: Localization and Exact Simulation of Brownian Motion Driven Stochastic Differential Equations; And Brownian Meanders, Importance Sampling and Un-biased Simulation of Diffusion Extremes. / The first essay considers generating sample paths of stochastic differential equations (SDE) using the Monte Carlo method. Discretization is a popular approximate approach to generating those paths: it is easy to implement but prone to simulation bias. This essay presents a new simulation scheme to exactly generate samples for SDEs. The key observation is that the law of a general SDE can be decomposed into a product of the law of standard Brownian motion and the law of a doubly stochastic Poisson process. An acceptance-rejection algorithm is devised based on the combination of this decomposition and a localization technique. The numerical results corroborates that the mean-square error of the proposed method is in the order of O(t⁻¹[superscript /]²), which is superior to the conventional discretization schemes. Furthermore, the proposed method also can generate exact samples for SDE with boundaries which the discretization schemes usually find difficulty in dealing with. / The second essay considers computing expected values of functions involving extreme values of diffusion processes. The conventional discretization Monte Carlo simulation schemes often converge very slowly. In this paper, we propose a Wiener measure decomposition-based approach to construct unbiased Monte Carlo estimators. Combined with the importance sampling technique and the celebrated Williams' path decomposition of Brownian motion, this approach transforms the task of simulating extreme values of a general diffusion process to the simulation of two Brownian meanders. The numerical experiments show the accuracy and efficiency of our Poisson-kernel unbiased estimators. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Huang, Zhengyu. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 107-115). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- SDEs and Discretization Methods --- p.4 / Chapter 1.3 --- The Beskos-Roberts Exact Simulation --- p.15 / Chapter 1.4 --- Major Contributions --- p.19 / Chapter 1.5 --- Organization --- p.26 / Chapter 2 --- Localization and Exact Simulation of SDEs --- p.27 / Chapter 2.1 --- Main Result: A Localization Technique --- p.27 / Chapter 2.1.1 --- Sampling of ζ --- p.33 / Chapter 2.1.2 --- Sampling of Wζ^(T-t) --- p.35 / Chapter 2.1.3 --- Sampling of the Bernoulli I --- p.38 / Chapter 2.1.4 --- Comparison Involving Infinite Sums --- p.40 / Chapter 2.2 --- Discussions --- p.43 / Chapter 2.2.1 --- One Extension: SDEs with Boundaries --- p.43 / Chapter 2.2.2 --- Simulation Efficiency --- p.45 / Chapter 2.2.3 --- Extension to Multi-dimensional SDE --- p.48 / Chapter 2.3 --- Numerical Examples --- p.52 / Chapter 2.3.1 --- Ornstein-Uhlenbeck Mean-Reverting Process --- p.52 / Chapter 2.3.2 --- A Double-Well Potential Model --- p.56 / Chapter 2.3.3 --- Cox-Ingersoll-Ross Square-Root Process --- p.56 / Chapter 2.3.4 --- Linear-Drift CEV-Type-Diffusion Model --- p.62 / Chapter 2.4 --- Appendix --- p.62 / Chapter 2.4.1 --- Simulation of Brownian Bridges --- p.62 / Chapter 2.4.2 --- Proofs of Main Results --- p.64 / Chapter 2.4.3 --- The Oscillating Property of the Series --- p.71 / Chapter 3 --- Unbiased Simulation of Diffusion Extremes --- p.79 / Chapter 3.1 --- A Wiener Measure Decomposition --- p.79 / Chapter 3.2 --- Brownian Meanders and Importance Sampler of Diffusion Extremes --- p.81 / Chapter 3.2.1 --- Exact Simulation of (θT, KT, WT) --- p.83 / Chapter 3.2.2 --- Simulating Importance Sampling Weight --- p.84 / Chapter 3.3 --- Some Extensions --- p.88 / Chapter 3.3.1 --- Variance Reduction --- p.88 / Chapter 3.3.2 --- Double Barrier Options --- p.90 / Chapter 3.4 --- Numerical Examples --- p.94 / Chapter 3.5 --- Appendix --- p.98 / Chapter 3.5.1 --- Brownian Bridges and Meanders --- p.98 / Chapter 3.5.2 --- Proofs of Main Results --- p.101 / Bibliography --- p.107