Comparison results for diffusions conditioned on positivity

1983 ◽  
Vol 20 (4) ◽  
pp. 766-777 ◽  
Author(s):  
Martin V. Day
Keyword(s):  
Diffusion Process ◽  
Conditional Probability ◽  
Comparison Theorem ◽  
Markov Diffusion ◽  
Comparison Results ◽  
Conditioned Diffusion ◽  
Initial Process

We consider a diffusion process on the reals subject to the conditional probability that the process is positive from t = 0 to the present. We establish comparison results between the conditioned diffusion and a second unconditioned Markov diffusion. One result allows the initial process to be non-Markov before conditioning. A stronger comparison theorem is shown to hold in the Markov case.

Comparison results for diffusions conditioned on positivity

1983 ◽  
Vol 20 (04) ◽  
pp. 766-777
Author(s):  
Martin V. Day
Keyword(s):  
Diffusion Process ◽  
Conditional Probability ◽  
Comparison Theorem ◽  
Markov Diffusion ◽  
Comparison Results ◽  
Conditioned Diffusion ◽  
Initial Process

We consider a diffusion process on the reals subject to the conditional probability that the process is positive from t = 0 to the present. We establish comparison results between the conditioned diffusion and a second unconditioned Markov diffusion. One result allows the initial process to be non-Markov before conditioning. A stronger comparison theorem is shown to hold in the Markov case.

DRIFT TRANSFORMATIONS OF SYMMETRIC DIFFUSIONS, AND DUALITY

2007 ◽  
Vol 10 (04) ◽  
pp. 613-631 ◽  
Author(s):  
P. J. FITZSIMMONS
Keyword(s):  
Diffusion Process ◽  
Dirichlet Form ◽  
Infinitesimal Generator ◽  
Probabilistic Approach ◽  
Additive Functionals ◽  
Excessive Measure ◽  
Girsanov’S Theorem ◽  
Markov Diffusion ◽  
Symmetry Measure

Starting with a symmetric Markov diffusion process X (with symmetry measure m and L2 (m) infinitesimal generator A) and a suitable core [Formula: see text] for the Dirichlet form of X, we describe a class of derivations defined on [Formula: see text]. Associated with each such derivation B is a drift transformation of X, obtained through Girsanov's theorem. The transformed process XB is typically non-symmetric, but we are able to show that if the "divergence" of B is positive, then m is an excessive measure for XB, and the L2 (m) infinitesimal generator of XB is an extension of f ↦ Af + B (f). The methods used are mainly probabilistic, and involve the notions of even and odd continuous additive functionals, and Nakao's stochastic divergence. These methods yield a probabilistic approach to the adjoint of the semigroup of XB, and in particular lead to a solution of a problem of W. Stannat.

Perceptions of Stuttering of Different Age Groups

2019 ◽  
Vol 4 (6) ◽  
pp. 1311-1315
Author(s):  
Sergey M. Kondrashov ◽  
John A. Tetnowski
Keyword(s):  
Age Groups ◽  
School Age Children ◽  
Clinical Implications ◽  
School Age ◽  
Fourth Edition ◽  
Self Perception ◽  
Behavioral Measures ◽  
Self Rating ◽  
Comparison Results ◽  
Subject Pool

Purpose The purpose of this study was to assess the perceptions of stuttering of school-age children who stutter and those of adults who stutter through the use of the same tools that could be commonly used by clinicians. Method Twenty-three participants across various ages and stuttering severity were administered both the Stuttering Severity Instrument–Fourth Edition (SSI-4; Riley, 2009 ) and the Wright & Ayre Stuttering Self-Rating Profile ( Wright & Ayre, 2000 ). Comparisons were made between severity of behavioral measures of stuttering made by the SSI-4 and by age (child/adult). Results Significant differences were obtained for the age comparison but not for the severity comparison. Results are explained in terms of the correlation between severity equivalents of the SSI-4 and the Wright & Ayre Stuttering Self-Rating Profile scores, with clinical implications justifying multi-aspect assessment. Conclusions Clinical implications indicate that self-perception and impact of stuttering must not be assumed and should be evaluated for individual participants. Research implications include further study with a larger subject pool and various levels of stuttering severity.

Sign in / Sign up

Export Citation Format

Share Document