Robust filtering: Correlated noise and multidimensional observation

In the late seventies, Clark [In Communication Systems and Random Process Theory (Proc. 2nd NATO Advanced Study Inst., Darlington, 1977) (1978) 721-734, Sijthoff & Noordhoff] pointed out that it would be natural for $\pi_t$, the solution of the stochastic filtering problem, to depend continuously on the observed data $Y=\{Y_s,s\in[0,t]\}$. Indeed, if the signal and the observation noise are independent one can show that, for any suitably chosen test function $f$, there exists a continuous map $\theta^f_t$, defined on the space of continuous paths $C([0,t],\mathbb{R}^d)$ endowed with the uniform convergence topology such that $\pi_t(f)=\theta^f_t(Y)$, almost surely; see, for example, Clark [In Communication Systems and Random Process Theory (Proc. 2nd NATO Advanced Study Inst., Darlington, 1977) (1978) 721-734, Sijthoff & Noordhoff], Clark and Crisan [Probab. Theory Related Fields 133 (2005) 43-56], Davis [Z. Wahrsch. Verw. Gebiete 54 (1980) 125-139], Davis [Teor. Veroyatn. Primen. 27 (1982) 160-167], Kushner [Stochastics 3 (1979) 75-83]. As shown by Davis and Spathopoulos [SIAM J. Control Optim. 25 (1987) 260-278], Davis [In Stochastic Systems: The Mathematics of Filtering and Identification and Applications, Proc. NATO Adv. Study Inst. Les Arcs, Savoie, France 1980 505-528], [In The Oxford Handbook of Nonlinear Filtering (2011) 403-424 Oxford Univ. Press], this type of robust representation is also possible when the signal and the observation noise are correlated, provided the observation process is scalar. For a general correlated noise and multidimensional observations such a representation does not exist. By using the theory of rough paths we provide a solution to this deficiency: the observation process $Y$ is "lifted" to the process $\mathbf{Y}$ that consists of $Y$ and its corresponding L\'{e}vy area process, and we show that there exists a continuous map $\theta_t^f$, defined on a suitably chosen space of H\"{o}lder continuous paths such that $\pi_t(f)=\theta_t^f(\mathbf{Y})$, almost surely.Comment: Published in at http://dx.doi.org/10.1214/12-AAP896 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Transient dynamics and structure of optimal excitations in thermocapillary spreading: Precursor film model

Linearized modal stability theory has shown that the thermocapillary spreading of a liquid film on a homogeneous, completely wetting surface can produce a rivulet instability at the advancing front due to formation of a capillary ridge. Mechanisms that drain fluid from the ridge can stabilize the flow against rivulet formation. Numerical predictions from this analysis for the film speed, shape, and most unstable wavelength agree remarkably well with experimental measurements even though the linearized disturbance operator is non-normal, which allows transient growth of perturbations. Our previous studies using a more generalized nonmodal stability analysis for contact lines models describing partially wetting liquids (i.e., either boundary slip or van der Waals interactions) have shown that the transient amplification is not sufficient to affect the predictions of eigenvalue analysis. In this work we complete examination of the various contact line models by studying the influence of an infinite and flat precursor film, which is the most commonly employed contact line model for completely wetting films. The maximum amplification of arbitrary disturbances and the optimal initial excitations that elicit the maximum growth over a specified time, which quantify the sensitivity of the film to perturbations of different structure, are presented. While the modal results for the three different contact line models are essentially indistinguishable, the transient dynamics and maximum possible amplification differ, which suggests different transient dynamics for completely and partially wetting films. These differences are explained by the structure of the computed optimal excitations, which provides further basis for understanding the agreement between experiment and predictions of conventional modal analysis

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

Investigation on Dabigatran Etexilate and Worsening of Renal Function in Patients with Atrial fibrillation : the IDEA Study

BACKGROUND AND OBJECTIVES: Warfarin-related nephropathy is an unexplained acute kidney injury, and may occur in patients with supratherapeutic INR, in the absence of overt bleeding. Similar findings have been observed in rats treated with dabigatran etexilate. We conducted a prospective study in dabigatran etexilate-treated patients to assess the incidence of dabigatran-related nephropathy and to investigate the possible correlation between dabigatran plasma concentration (DPC) and worsening renal function. METHOD: One hundred and seven patients treated long term with dabigatran etexilate for non-valvular atrial fibrillation (NVAF) were followed up for 90 days. DPC, serum creatinine (SCr) and serum cystatin C were prospectively measured. Ninety five patients had complete follow-up data and were evaluable for primary endpoint. RESULTS: Eleven patients had supratherapeutic DPC, defined as DPC higher than 200 ng/ml at study enrolment, but at the end of follow-up no patient showed a persistent increase in SCr. No patients experienced acute kidney injury. CONCLUSIONS: Our study shows that no persistent renal detrimental effect is associated with dabigatran treatment. An increase in SCr during dabigatran treatment is reversible and it seems to be unrelated to dabigatran itself

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

Continuous Equilibrium in Affine and Information-Based Capital Asset Pricing Models

We consider a class of generalized capital asset pricing models in continuous time with a finite number of agents and tradable securities. The securities may not be sufficient to span all sources of uncertainty. If the agents have exponential utility functions and the individual endowments are spanned by the securities, an equilibrium exists and the agents' optimal trading strategies are constant. Affine processes, and the theory of information-based asset pricing are used to model the endogenous asset price dynamics and the terminal payoff. The derived semi-explicit pricing formulae are applied to numerically analyze the impact of the agents' risk aversion on the implied volatility of simultaneously-traded European-style options.Comment: 24 pages, 4 figure

5.3 Left Ventricular Mass Independently Contributes to Long-Term Risk of Cardiovascular Morbidity and Mortality in a General Population: Data From the PAMELA Study

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A hybrid soft material robotic end-effector for reversible in-space assembly of strut components

Based on the NASA in-Space Assembled Telescope (iSAT) study (Bulletin of the American Astronomical Society, 2019, 51, 50) which details the design and requirements for a 20-m parabolic in-space telescope, NASA Langley Research Center (LaRC) has been developing structural and robotic solutions to address the needs of building larger in-space assets. One of the structural methods studied involves stackable and collapsible modular solutions to address launch vehicle volume constraints. This solution uses a packing method that stacks struts in a dixie-cup like manner and a chemical composite bonding technique that reduces weight of the structure, adds strength, and offers the ability to de-bond the components for structural modifications. We present in this paper work towards a soft material robot end-effector, capable of suppling the manipulability, pressure, and temperature requirements for the bonding/de-bonding of these conical structural components. This work is done to investigate the feasibility of a hybrid soft robotic end-effector actuated by Twisted and Coiled Artificial Muscles (TCAMs) for in-space assembly tasks. TCAMs are a class of actuator which have garnered significant recent research interest due to their allowance for high force to weight ratio when compared to other popular methods of actuation within the field of soft robotics, and a muscle-tendon actuation design using TCAMs leads to a compact and lightweight system with controllable and tunable behavior. In addition to the muscle-tendon design, this paper also details the early investigation of an induction system for adhesive bonding/de-bonding and the sensors used for benchtop design and testing. Additionally, we discuss the viability of Robotic Operating System 2 (ROS2) and Gazebo modeling environments for soft robotics as they pertain to larger simulation efforts at LaRC. We show real world test results against simulation results for a method which divides the soft, continuous material of the end-effector into discrete links connected by spring-like joints

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