Large deviations for perturbed Gaussian processes and logarithmic asymptotic estimates for some exit probabilities

The main results in this paper concern large deviations for families of non-Gaussian processes obtained as suitable perturbations of continuous centered multivariate Gaussian processes which satisfy a large deviation principle. We present some corollaries and, as a consequence, we obtain logarithmic asymptotic estimates for exit probabilities from suitable halfspaces and quadrants.Comment: 22 page

Reducing the rate and duration of Re-ADMISsions among patients with unipolar disorder and bipolar disorder using smartphone-based monitoring and treatment -- the RADMIS trials: study protocol for two randomized controlled trials

Abstract Background Unipolar and bipolar disorder combined account for nearly half of all morbidity and mortality due to mental and substance use disorders, and burden society with the highest health care costs of all psychiatric and neurological disorders. Among these, costs due to psychiatric hospitalization are a major burden. Smartphones comprise an innovative and unique platform for the monitoring and treatment of depression and mania. No prior trial has investigated whether the use of a smartphone-based system can prevent re-admission among patients discharged from hospital. The present RADMIS trials aim to investigate whether using a smartphone-based monitoring and treatment system, including an integrated clinical feedback loop, reduces the rate and duration of re-admissions more than standard treatment in unipolar disorder and bipolar disorder. Methods The RADMIS trials use a randomized controlled, single-blind, parallel-group design. Patients with unipolar disorder and patients with bipolar disorder are invited to participate in each trial when discharged from psychiatric hospitals in The Capital Region of Denmark following an affective episode and randomized to either (1) a smartphone-based monitoring system including (a) an integrated feedback loop between patients and clinicians and (b) context-aware cognitive behavioral therapy (CBT) modules (intervention group) or (2) standard treatment (control group) for a 6-month trial period. The trial started in May 2017. The outcomes are (1) number and duration of re-admissions (primary), (2) severity of depressive and manic (only for patients with bipolar disorder) symptoms; psychosocial functioning; number of affective episodes (secondary), and (3) perceived stress, quality of life, self-rated depressive symptoms, self-rated manic symptoms (only for patients with bipolar disorder), recovery, empowerment, adherence to medication, wellbeing, ruminations, worrying, and satisfaction (tertiary). A total of 400 patients (200 patients with unipolar disorder and 200 patients with bipolar disorder) will be included in the RADMIS trials. Discussion If the smartphone-based monitoring system proves effective in reducing the rate and duration of re-admissions, there will be basis for using a system of this kind in the treatment of unipolar and bipolar disorder in general and on a larger scale. Trial registration ClinicalTrials.gov, ID: NCT03033420 . Registered 13 January 2017. Ethical approval has been obtained

Asymptotic results for finite superpositions of Ornstein–Uhlenbeck processes

A model of intermittency based on superposition of Lévy driven Ornstein–Uhlenbeck processes is studied in [6]. In particular, as shown in Theorem 5.1 in that paper, finite superpositions obey a (sample path) central limit theoremunder suitable hypotheses. In this paper we prove large (and moderate) deviation results associated with this central limit theorem

Exponential tightness for Gaussian processes, with applications to some sequences of weighted means

Exponential tightness plays a crucial role in large deviations; in fact this condition is often required to obtain the large deviation principle for a sequence of random variables taking values on an infinite dimensional topological space. In this paper we present some conditions which yield the exponential tightness of a sequence of continuous Gaussian processes. Moreover we check these conditions for some sequences of weighted means

Asymptotic results for certain first-passage times and areas of renewal processes

We consider the process {x − N(t) : t ≥ 0}, where x ∈ R+ and {N(t) :t ≥ 0} is a renewal process with light-tailed distributed holding times. We are interested in the joint distribution of (τ(x),A(x)) where τ(x) is the first-passage time of {x−N(t) : t ≥ 0} to reach zero or a negative value, and A(x) := \int_0^{τ(x)} (x−N(t))dt is the corresponding first-passage (positive) area swept out by the process {x−N(t) :t ≥ 0}. We remark that we can define the sequence {(τ(n),A(n)) : n ≥ 1} by referring to the concept of integrated random walk. Our aim is to prove asymptotic results as x→∞ in the fashion of large (and moderate) deviations

Large deviations for a class of counting processes and some statistical applications

The aim of this paper is to prove results on large deviations for a class of counting processes, and to illustrate some statistical applications.We also present a generalization of the results for a class of compound processes. The statistical applications describe the asymptotic behavior of some issues concerning two hypothesis testing problems, and the logarithmic rates are expressed in terms of the large deviation rate function

Large deviations for estimators of the parameters of a neuronal response latency model

We consider a model in the literature for the neuronal activity with response latency. We present large deviation results for two sequences of estimators of some unknown parameters. We also present a large deviation result for the posterior distributions in the Bayesian setting