Intrinsic expansions for averaged diffusion processes

We show that the rate of convergence of asymptotic expansions for solutions of SDEs is generally higher in the case of degenerate (or partial) diffusion compared to the elliptic case, i.e. it is higher when the Brownian motion directly acts only on some components of the diffusion. In the scalar case, this phenomenon was already observed in (Gobet and Miri 2014) using Malliavin calculus techniques. In this paper, we provide a general and detailed analysis by employing the recent study of intrinsic functional spaces related to hypoelliptic Kolmogorov operators in (Pagliarani et al. 2016). Relevant applications to finance are discussed, in particular in the study of path-dependent derivatives (e.g. Asian options) and in models incorporating dependence on past information

Evidence for Disk Photoevaporation Driven by the Central Star

The lifetime of isolated protoplanetary disks is thought to be set by the combination of viscous accretion and photoevaporation driven by stellar high-energy photons. Observational evidence for magnetospheric accretion in young sun-like stars is robust. Here we report the first observational evidence for disk photoevaporation driven by the central star. We acquired high-resolution (R~30,000) spectra of the [NeII] 12.81 micron line from 7 circumstellar disks using VISIR on Melipal/VLT. We show that the 3 transition disks in the sample all have [NeII] line profiles consistent with those predicted by a photoevaporative flow driven by stellar extreme UV photons. The ~6 km/s blue-shift of the line from the almost face-on disk of TW Hya is clearly inconsistent with emission from a static disk atmosphere and convincingly points to the presence of a photoevaporative wind. We do not detect any [NeII] line close to the stellar velocity from the sample of classical optically thick (non-transition) disks. We conclude that most of the spectrally unresolved [NeII] emission in these less evolved systems arises from jets/outflows rather than from the disk. The pattern of the [NeII] detections and non-detections suggests that extreme UV-driven photoevaporation starts only at a later stage in the disk evolution.Comment: accepted for publication to Ap

Gamma-GQM Time Headway Model: Endogenous Effects in Rural Two-lane Two-way Roads

AbstractStudy of vehicle time headway distributions is essential in many traffic engineering applications, such as capacity and level of service analysis and, in recent years, in the fields of vehicle generation in traffic micro-simulation models and driving simulation applications. This paper presents results from an experimental analysis of vehicle time headway distributions on two-lane two-way rural roads. Analysis focused on estimating a well-known model, the gamma-generalized queuing model (gamma-GQM). A trendless analysis of observed time headways was also carried out. The endogenous traffic parameters considered as affecting time headway distributions were flow rate and flow composition (percentage of heavy vehicles). Exogenous conditions, such as weather and geometric futures, were common to all time periods and cross-sections analysed. Gamma-GQM pdf appears to be very suitable for representing real headway distributions in all the analysed situations; it fits real-time headway distributions well, despite flow rate range and traffic composition (range of percentage of heavy vehicles)

The Photoevaporative Wind from the Disk of TW Hya

Photoevaporation driven by the central star is expected to be a ubiquitous and important mechanism to disperse the circumstellar dust and gas from which planets form. Here, we present a detailed study of the circumstellar disk surrounding the nearby star TW Hya and provide observational constraints to its photoevaporative wind. Our new high-resolution (R ~ 30,000) mid-infrared spectroscopy in the [Ne II] 12.81 {\mu}m line confirms that this gas diagnostic traces the unbound wind component within 10AU from the star. From the blueshift and asymmetry in the line profile, we estimate that most (>80%) of the [Ne II] emission arises from disk radii where the midplane is optically thick to the redshifted outflowing gas, meaning beyond the 1 or 4AU dust rim inferred from other observations. We re-analyze high-resolution (R ~ 48, 000) archival optical spectra searching for additional transitions that may trace the photoevaporative flow. Unlike the [Ne II] line, optical forbidden lines from OI, SII, and MgI are centered at the stellar velocity and have symmetric profiles. The only way these lines could trace the photoevaporative flow is if they arise from a disk region physically distinct from that traced by the [Ne II] line, specifically from within the optically thin dust gap. However, the small (~10 km/s) FWHM of these lines suggest that most of the emitting gas traced at optical wavelengths is bound to the system rather than unbound. We discuss the implications of our results for a planet-induced versus a photoevaporation-induced gap.Comment: Accepted for publication in Ap

A Search for Companions to Brown Dwarfs in the Taurus and Chamaeleon Star Forming Regions

We present the results of a search for companions to young brown dwarfs in the Taurus and Chamaeleon I star forming regions (1/2-3 Myr). We have used WFPC2 on board HST to obtain F791W and F850LP images of 47 members of these regions that have spectral types of M6-L0 (0.01-0.1 Msun). An additional late-type member of Taurus, FU Tau (M7.25+M9.25), was also observed with adaptive optics at Keck Observatory. We have applied PSF subtraction to the primaries and have searched the resulting images for objects that have colors and magnitudes that are indicative of young low-mass objects. Through this process, we have identified promising candidate companions to 2MASS J04414489+2301513 (rho=0.105"/15 AU), 2MASS J04221332+1934392 (rho=0.05"/7 AU), and ISO 217 (rho=0.03"/5 AU). We reported the discovery of the first candidate in a previous study, showing that it has a similar proper motion as the primary through a comparison of astrometry measured with WFPC2 and Gemini adaptive optics. We have collected an additional epoch of data with Gemini that further supports that result. By combining our survey with previous high-resolution imaging in Taurus, Chamaeleon, and Upper Sco (10 Myr), we measure binary fractions of 14/93 = 0.15+0.05/-0.03 for M4-M6 (0.1-0.3 Msun) and 4/108 = 0.04+0.03/-0.01 for >M6 (10 AU. Given the youth and low density of these three regions, the lower binary fraction at later types is probably primordial rather than due to dynamical interactions among association members. The widest low-mass binaries (>100 AU) also appear to be more common in Taurus and Chamaeleon than in the field, which suggests that the widest low-mass binaries are disrupted by dynamical interactions at >10 Myr, or that field brown dwarfs have been born predominantly in denser clusters where wide systems are disrupted or inhibited from forming.Comment: Astrophysical Journal, in pres