On small time asymptotics for rough differential equations driven by fractional Brownian motions

We survey existing results concerning the study in small times of the density of the solution of a rough differential equation driven by fractional Brownian motions. We also slightly improve existing results and discuss some possible applications to mathematical finance.Comment: This is a survey paper, submitted to proceedings in the memory of Peter Laurenc

Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces II

The strong convergence of Wong-Zakai approximations of the solution to the reflecting stochastic differential equations was studied in [2]. We continue the study and prove the strong convergence under weaker assumptions on the domain.Comment: To appear in "Stochastic Analysis and Applications 2014-In Honour of Terry Lyons", Springer Proceedings in Mathematics and Statistic

Numerical Schemes for Rough Parabolic Equations

This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0, 1) perturbed by a non-linear rough signal. It is the continuation of [8, 7], where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H \textgreater{} 1/3.Comment: Applied Mathematics and Optimization, 201

From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the L\'evy area of fractional Brownian motion with Hurst index α∈(1/8,1/4)\alpha\in(1/8,1/4)

{Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\alpha<1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a difficult task because of the low H\"older regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates, and call for an extension of Gaussian tools such as for instance the Malliavin calculus. After a first introductory paper \cite{MagUnt1}, this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as L\'evy area

Multiscale Systems, Homogenization, and Rough Paths:VAR75 2016: Probability and Analysis in Interacting Physical Systems

In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classical approaches, the assumptions on the fast flow are very mild. We survey the origins of this theory and then revisit and improve the analysis of Kelly-Melbourne [Ann. Probab. Volume 44, Number 1 (2016), 479-520], taking into account recent progress in $p$-variation and c\`adl\`ag rough path theory.Comment: 27 pages. Minor corrections. To appear in Proceedings of the Conference in Honor of the 75th Birthday of S.R.S. Varadha

Convergence of multi-dimensional quantized SDESDE's

We quantize a multidimensional $SDE$ (in the Stratonovich sense) by solving the related system of $ODE$'s in which the $d$-dimensional Brownian motion has been replaced by the components of functional stationary quantizers. We make a connection with rough path theory to show that the solutions of the quantized solutions of the $ODE$ converge toward the solution of the $SDE$. On our way to this result we provide convergence rates of optimal quantizations toward the Brownian motion for $\frac 1q$-H\" older distance, $q>2$, in $L^p(\P)$.Comment: 43 page

What hinders the uptake of computerized decision support systems in hospitals? A qualitative study and framework for implementation

Background: Advanced Computerized Decision Support Systems (CDSSs) assist clinicians in their decision-making process, generating recommendations based on up-to-date scientific evidence. Although this technology has the potential to improve the quality of patient care, its mere provision does not guarantee uptake: even where CDSSs are available, clinicians often fail to adopt their recommendations. This study examines the barriers and facilitators to the uptake of an evidence-based CDSS as perceived by diverse health professionals in hospitals at different stages of CDSS adoption. Methods: Qualitative study conducted as part of a series of randomized controlled trials of CDSSs. The sample includes two hospitals using a CDSS and two hospitals that aim to adopt a CDSS in the future. We interviewed physicians, nurses, information technology staff and members of the boards of directors (n=30). We used a constant comparative approach to develop a framework for guiding implementation. Findings: We identified six clusters of experiences of, and attitudes towards CDSSs, which we label as ‘positions’. The six positions represent a gradient of acquisition of control over CDSSs (from low to high) and are characterized by different types of barriers to CDSS uptake. The most severe barriers (prevalent in the first positions) include clinicians’ perception that the CDSSs may reduce their professional autonomy or may be used against them in the event of medical-legal controversies. Moving towards the last positions, these barriers are substituted by technical and usability problems related with the technology interface. When all barriers are overcome, CDSSs are perceived as a working tool at the service of its users, integrating clinicians’ reasoning and fostering organizational learning. Discussion: Barriers and facilitators to the use of CDSSs are dynamic and may exist prior to their introduction in clinical contexts; providing a static list of obstacles and facilitators, irrespective of the specific implementation phase and context, may not be sufficient or useful to facilitate uptake. Factors such as clinicians’ attitudes towards scientific evidences and guidelines, the quality of inter-disciplinary relationships and an organizational ethos of transparency and accountability need to considered when exploring the readiness of a hospital to adopt CDSSs.This work is supported by the Italian Ministry of Health (GR-2009-1606736), Regione Lombardia (D.R.G. IX/4340 26/10/2012), and the Wellcome Trust (WT097899)

Improving Plasma Actuator Thrust At Low Pressure Through Geometric Variation

The force production and power consumption of plasma actuators with varying electrode geometries was measured. The geometries were varied by changing the length of the exposed and buried electrodes as well as varying the chord-wise gap between the electrodes. Each actuator was driven with a 5 kHz sine wave at 16 kVpp, and operated at pressures ranging from 10-101 kPa, which corresponds to altitudes from 16,000 m to sea level. The electric eld of each con guration was also modeled using Maxwell Ansoft. Increasing the length of the buried electrode was found to have the greatest e ect on thrust production especially at low pressure. Actuators with 75 mm buried electrodes produced an average of 26% more thrust at all pressures and 34% more thrust at 20-40 kPa than the traditional 15 mm buried electrode. The gap study revealed that actuators with a 1 mm gap produced the most force at all pressures. All actuator designs were found to have a similar linear relationship between their e ectivenesses and operating pressure

Valuation of volatility derivatives as an inverse problem

Ground-breaking recent work by Carr and Lee extends well-known results for variance swaps to arbitrary functions of realized variance, provided a zero-correlation assumption is made. We give a detailed mathematical analysis of some of their computations and work out the cases of volatility swaps and calls on variance. The latter leads to an ill-posed problem that we solve using regularization techniques. The sum is divergent, that means we can do something Heaviside†