Mean first-passage time for system driven by the coin-toss square wave

We study the mean-first-passage-time problem for systems driven by the coin-toss square-wave signal. Exact analytic solutions are obtained for the driftless case. We also obtain approximate solutions for the potential case. The mean-first-passage time exhibits discontinuities and a remarkable nonsmooth oscillatory behavior which, to our knowledge, has not been observed for other kinds of driving noise.

Law Enforcement Careers with Motor Vehicle Enforcement, October 17, 2008

A motor vehicle officer is peace officer whose primary duty it is to enforce all state and federal regulation that apply to commercial vehicles travels Iowa's roadways.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Homicide-suicide cases in Switzerland and their impact on the Swiss Weapon Law.

Homicide followed by the suicide of the offender is a well-known phenomenon. In most cases, it takes place in the context of the so-called "family tragedies." A recent series of such family tragedies in Switzerland prompted an intensive debate in the media and the Swiss government concerning the Swiss Weapon Law, in particular the requirement to keep personal army weapons at home. The present study of Homicide-Suicide cases in Switzerland, thus focuses on the role played by guns, especially military weapons, in such crimes. We investigated retrospectively 75 cases of Homicide-Suicide, comprising 172 individuals and spanning a period of 23 years in western and central Switzerland. Our results show that if guns were used in 76% of the cases, army weapons were the cause of death in 25% of the total. In 28% of the deaths caused by a gunshot, the exact type of the gun and its origin could not be determined. Thus, the majority of Homicide-Suicide cases in Switzerland involve the use of guns. The exact percentage of cases were military weapons were involved could not be defined. In our opinion, a stricter weapons law, restricting access to firearms, would be a factor of prevention of Homicide- Suicide cases in Switzerland.

Resonating-valence-bond theory for the square-planar lattice

The short-range resonating-valence-bond (RVB) wave function with nearest-neighbor (NN) spin pairings only is investigated as a possible description for the Heisenberg model on a square-planar lattice. A type of long-range order associated to this RVB Ansatz is identified along with some qualitative consequences involving lattice distortions, excitations, and their coupling.

Estimation of the correlation structure of crustal velocity heterogeneity from seismic reflection data

Numerous sources of evidence point to the fact that heterogeneity within the Earth's deep crystalline crust is complex and hence may be best described through stochastic rather than deterministic approaches. As seismic reflection imaging arguably offers the best means of sampling deep crustal rocks in situ, much interest has been expressed in using such data to characterize the stochastic nature of crustal heterogeneity. Previous work on this problem has shown that the spatial statistics of seismic reflection data are indeed related to those of the underlying heterogeneous seismic velocity distribution. As of yet, however, the nature of this relationship has remained elusive due to the fact that most of the work was either strictly empirical or based on incorrect methodological approaches. Here, we introduce a conceptual model, based on the assumption of weak scattering, that allows us to quantitatively link the second-order statistics of a 2-D seismic velocity distribution with those of the corresponding processed and depth-migrated seismic reflection image. We then perform a sensitivity study in order to investigate what information regarding the stochastic model parameters describing crustal velocity heterogeneity might potentially be recovered from the statistics of a seismic reflection image using this model. Finally, we present a Monte Carlo inversion strategy to estimate these parameters and we show examples of its application at two different source frequencies and using two different sets of prior information. Our results indicate that the inverse problem is inherently non-unique and that many different combinations of the vertical and lateral correlation lengths describing the velocity heterogeneity can yield seismic images with the same 2-D autocorrelation structure. The ratio of all of these possible combinations of vertical and lateral correlation lengths, however, remains roughly constant which indicates that, without additional prior information, the aspect ratio is the only parameter describing the stochastic seismic velocity structure that can be reliably recovered.

Report on the Iowa Law Enforcement Academy for the year ended June 30, 2011

Report on the Iowa Law Enforcement Academy for the year ended June 30, 2011

Linear least squares estimation of the first order moving average parameter

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed

Harassment in Education: It's Against the Law, 2011

Harassment is illegal in all areas protected by Iowa Code Chapter 216. This includes education, employment, public accommodations, credit and housing. Acts of harassment take place every day in schools across the country. Frequently these acts, even if reported to administration, are dismissed as harmless, as "kids will be kids," or as "no big deal." Many people do not realize that harassment that interferes with a person's educational progress is illegal, just as it is illegal in the workplace.

What the Law Requires Accessible Multi-family Housing in Iowa, Janaury 2001

For people with disabilities, however, housing options have been limited. Today, state and federal laws are changing this. Who will benefit? All of us. For “accessibility” is an issue that, at one time or another, affects us all. This is true whether _ temporarily or permanently _ we use wheelchairs, need grab bars, cannot climb stairs, require easy-to-reach shelves, or rely on easy-to-navigate living spaces. The primary purpose of accessible housing law is to prevent discrimination against people with disabilities, but the end result is a living environment that is more usable for everyone. For example, both the very young and the very old will find an accessible dwelling more comfortable. People with temporary limitations due to injury or illness will find it easier to live in. Such a home will be more welcoming to guests with disabilities.

Sexual Orientation Gender Indentity, and Iowa's Safe Schools Law, 2007

Another recently enacted law is the Iowa Safe Schools Law. Effective September 1, 2007, Iowa Code Chapter 280 requires both public and private schools to establish policies prohibiting harassment and bullying against students by employees, school volunteers, or other students. Sexual Orientation and Gender identity are covered under the Safe Schools Law. Students may now seek remedies under both Chapter 216 and Chapter 280.

Sexual Orientation & Gender Indentity: A Housing Provider’s Guide to Iowa Law Compliance, 2007

Effective July 1, 2007, the Iowa Civil Rights Act (Iowa Code Chapter 216) was expanded to add sexual orientation and gender identity to the list of protected classes. It is now ILLEGAL in Iowa to discriminate against a person because of his/her sexual orientation or gender identity.

Sexual Orientation & Gender Identity: A Public Accommodations Provider’s Guide to Iowa Law, 2007

Effective July 1, 2007, the Iowa Civil Rights Act (Iowa Code Chapter 216) was expanded to add sexual orientation and gender identity to the list of protected classes. It is now ILLEGAL in Iowa to discriminate against a person because of his/her sexual orientation or gender identity.