Stochastic Calculus with respect to Gaussian Processes

Stochastic integration with respect to Gaussian processes, such as fractional Brownian motion (fBm) or multifractional Brownian motion (mBm), has raised strong interest in recent years, motivated in particular by applications in finance, Internet traffic modeling and biomedicine. The aim of this work to define and develop, using White Noise Theory, an anticipative stochastic calculus with respect to a large class of Gaussian processes, denoted G, that contains, among many other processes, Volterra processes (and thus fBm) and also mBm. This stochastic calculus includes a definition of a stochastic integral, It\^o formulas (both for tempered distributions and for functions with sub-exponential growth), a Tanaka Formula as well as a definition, and a short study, of (both weighted and non weighted) local times of elements of G . In that view, a white noise derivative of any Gaussian process G of G is defined and used to integrate, with respect to G, a large class of stochastic processes, using Wick products. A comparison of our integral wrt elements of G to the ones provided by Malliavin calculus in [AMN01] and by It\^o stochastic calculus is also made. Moreover, one shows that the stochastic calculus with respect to Gaussian processes provided in this work generalizes the stochastic calculus originally proposed for fBm in [EVdH03, BS{\O}W04, Ben03a] and for mBm in [LLV14, Leb13, LLVH14]. Likewise, it generalizes results given in [NT06] and some results given in [AMN01]. In addition, it offers alternative conditions to the ones required in [AMN01] when one deals with stochastic calculus with respect to Gaussian processes.Comment: (26/07/2014). Previously this work appeared as arXiv:1703.08393 which was incorrectly submitted as a new paper (and has now been withdrawn

People, Place, Process: Unpacking Local Efforts To Produce Social Sustainability

This three-paper dissertation seeks to understand the factors that drive social sustainability in local contexts, giving attention to institutional efforts of local governments and nonprofit agencies as well as the interdependence between the built environment and collective action efforts. It marries two separate literatures, in public affairs and urban studies, by conceptualizing the relationships between the way spaces have been planned and designed to function and they ways they are lived in and governed. The first paper measures the relationship between modes of housing settlement within a city and the number of social sustainability policies a city adopts, finding a positive and statistically significant relationship between the dominance of single-family detached housing and the adoption of fewer policies. Paper two is a process tracing effort to understand the ways that a city that was historically designed to be dominated by single-family detached homes and automotive access can promote social sustainability through restorative justice efforts. Lastly, the third paper seeks to understand how members of a progressive nonprofit group who live in a region dominated by low-density housing and lack of public transit continue to engage in interactive, community building efforts. v Overall, this dissertation speaks to the existing literature on the relationship between spatial and social aspects of urban areas and adds to our understanding of how the production of social sustainability is tied to the physical landscape of an area

I is an Other : An Exploration of the Development of Childhood and Adolescent Self-Concept

A multidisciplinary project that combines original empirical research with an analysis of two Modernist novels, The Waves by Virginia Woolf and A Portrait of the Artist as a Young Man by James Joyce

Misinformation in Consumer Product Reviews and their Effect on Resonance Marketing

The purpose of this study is to test the theory of resonance marketing in an experimental setting. We want to see the effects product reviews can have on consumers, specifically how reviews can affect a consumer’s perception of a product’s quality. We will use beer, a well-­‐known resonance marketing product, and conduct taste tests under varying conditions where the treatments involve reviews and the control does not. We will use subjects that are the target of resonance marketing, namely consumers with defined preferences and a willingness to pay for high quality products