ON COLLISION LOCAL TIME OF TWO INDEPENDENT FRACTIONAL ORNSTEIN-UHLENBECK PROCESSES

In this article, we study the existence of collision local time of two indepen- dent d-dimensional fractional Ornstein-Uhlenbeck processes X＋^H1 and Xt^H2 with different parameters Hi ∈ （0, 1）,i = 1, 2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its＇ chaos expansion. Key words Collision local time; fractional Ornstein-Uhlenbeck processes; generalized white noise functionals; choas expansion

Fractional Brownian Motion and Sheet as White Noise Functionals

In this short note, we show that it is more natural to look the fractional Brownian motion as functionals of the standard white noises, and the fractional white noise calculus developed by Hu and Фksendal follows directly from the classical white noise functional calculus. As examples we prove that the fractional Girsanov formula, the Ito type integrals and the fractional Black-Scholes formula are easy consequences of their classical counterparts. An extension to the fractional Brownian sheet is also briefly discussed.

Anisotropic Fractional Brownian Random Fields as White Noise Functionals

This investigation aims at a new construction of anisotropic fractional Brownian random fields by the white noise approach. Moreover, we investigate its distribution and sample properties （stationariness of increments, self-similarity, sample continuity） which will furnish some useful views to future applications.

Investigation of white matter functional networks underlying different behavioral profiles in attention-deficit/hyperactivity disorder

Background Cortical functional network alterations have been widely accepted as the neural basis of attention-deficit/hyperactivity disorder(ADHD).Recently,white matter has also been recognized as a novel neuroimaging marker of psychopathology and has been used as a complement to cortical functional networks to investigate brain–behavior relationships.However,disorder-specific features of white matter functional networks(WMFNs)are less well understood than those of gray matter functional networks.In the current study,we constructed WMFNs using a new strategy to characterize behavior-related network features in ADHD.Methods We recruited 46 drug-nale boys with ADHD and 46 typically developing(TD)boys,and used clustering analysis on restingstate functional magnetic resonance imaging data to generate WMFNs in each group.Intrinsic activity within each network was extracted,and the associations between network activity and behavior measures were assessed using correlation analysis.Results Nine WMFNs were identified for both ADHD and TD participants.However,boys with ADHD showed a splitting of the inferior corticospinal–cerebellar network and lacked a cognitive control network.In addition,boys with ADHD showed increased activity in the dorsal attention network and somatomotor network,which correlated positively with attention problems and hyperactivity symptom scores,respectively,while they presented decreased activity in the frontoparietal network and frontostriatal network in association with poorer performance in response inhibition,working memory,and verbal fluency.Conclusions We discovered a dual pattern of white matter network activity in drug-nale ADHD boys,with hyperactive symptom-related networks and hypoactive cognitive networks.These findings characterize two distinct types of WMFN in ADHD psychopathology.