Smoothness of the density for solutions to Gaussian rough differential equations

We consider stochastic differential equations of the form $dY_t=V(Y_t)\,dX_t+V_0(Y_t)\,dt$ driven by a multi-dimensional Gaussian process. Under the assumption that the vector fields $V_0$ and $V=(V_1,\ldots,V_d)$ satisfy H\"{o}rmander's bracket condition, we demonstrate that $Y_t$ admits a smooth density for any $t\in(0,T]$, provided the driving noise satisfies certain nondegeneracy assumptions. Our analysis relies on relies on an interplay of rough path theory, Malliavin calculus and the theory of Gaussian processes. Our result applies to a broad range of examples including fractional Brownian motion with Hurst parameter $H>1/4$, the Ornstein-Uhlenbeck process and the Brownian bridge returning after time $T$.Comment: Published in at http://dx.doi.org/10.1214/13-AOP896 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

A dual algorithm for stochastic control problems : Applications to Uncertain Volatility Models and CVA

We derive an algorithm in the spirit of Rogers [SIAM J. Control Optim., 46 (2007), pp. 1116--1132] and Davis and Burstein [Stochastics Stochastics Rep., 40 (1992), pp. 203--256] that leads to upper bounds for stochastic control problems. Our bounds complement lower biased estimates recently obtained in Guyon and Henry-Labordère [J. Comput. Finance, 14 (2011), pp. 37--71]. We evaluate our estimates in numerical examples motivated by mathematical finance. Read More: http://epubs.siam.org/doi/10.1137/15M101994

On the integration of weakly geometric rough paths

We close a gap in the theory of integration for weakly geometric rough paths in the in…nite-dimensional setting. We show that the integral of a weakly geometric rough path against a su¢ ciently regular one form is, once again, a weakly geometric rough path

Gravitational wave behavior at a vacuum-matter interface

In classical electrodynamics, boundary conditions of the E and B fields are derived from Maxwell\u27s equations, which are used to derive the Fresnel equations describing the behavior of a wave at an interface between media with given indices of refraction. Though electrodynamics and gravity are in some instances strikingly analogous, boundary conditions in general relativity are somewhat more opaque. We will see that while while continuity of the metric must be true in general, discontinuity of the extrinsic curvature of spacetime, while allowed by the Einstein field equations, results in a singularity in the energy-momentum tensor. This singularity is interpreted as a surface mass density. Unlike in electrodynamics, there is an additional refractive effect of the spacetime metric. Its origin considered, a gravitational refractive index will be treated similarly to the electromagnetic refractive index. Attempts to derive gravitational Fresnel equations follow

Lisa Ben and Queer Rhetorical Reeducation in Post-war Los Angeles

“Lisa Ben and Queer Rhetorical Reeducation in Post-war Los Angeles” combines historiography and queer rhetorical analysis to examine the ways that discourse circulated and rhetorically educated audiences and readers about homosexuality in post-war Los Angeles, California (and the wider United States), a time and place that was influenced by dominant discourses around censorship, morality, and nationalism. I examine historical documents, such as newspaper articles, song lyrics, films and plays, and magazine articles, and I put these in conversation with multiple texts by one woman: Lisa Ben. Ben is a figurehead in this dissertation because she endeavored to rhetorically reeducate readers and audiences about the sexological and homophobic discourses that circulated in her lifetime (1921-2015). By arguing that Ben performs queer rhetorical reeducation through generating and circulating texts that both critique and disrupt dominant discourses around “the homosexual,” my dissertation engages queer rhetorical analysis to extend feminist recovery efforts and thus reads Ben’s writing as a move to rhetorically educate readers in the context of strict rules for discourse circulation about sexuality. I argue that Lisa Ben interrupts the dissemination of dominant discourses about homosexuality by circulating alternative texts that expose and critique power within discourses about normality and abnormality, offering a queer alternative to such messages, and putting that alternative into circulation. Finally, I extend this queer rhetorical reeducation to today, imagining how I and other queer historians, rhetorical scholars, and creatives may carry the torch of queer rhetorical reeducation in the future by historicizing Lisa Ben and her rhetorical contributions