SELF-INTERSECTION LOCAL TIME FOR ${\mathcal S}' ({\mathbb R}^d)$-WIENER PROCESSES AND RELATED ORNSTEIN–UHLENBECK PROCESSES

1999 ◽  
Vol 02 (04) ◽  
pp. 569-615 ◽  
Author(s):  
TOMASZ BOJDECKI ◽  
LUIS G. GOROSTIZA
Keyword(s):  
Random Field ◽  
Local Time ◽  
Fourier Transforms ◽  
Stable Process ◽  
Local Times ◽  
Spherically Symmetric ◽  
Homogeneous Random Field ◽  
Intersection Local Time ◽  
Wiener Processes ◽  
First Results

Existence and continuity results are obtained for self-intersection local time of [Formula: see text]-valued Ornstein–Uhlenbeck processes [Formula: see text], where X0 is Gaussian, Wt is an [Formula: see text]-Wiener process (independent of X0), and T't is the adjoint of a semigroup Tt on [Formula: see text]. Two types of covariance kernels for X0 and for W are considered: square tempered kernels and homogeneous random field kernels. The case where Tt corresponds to the spherically symmetric α-stable process in ℝd, α∈(0,2], is treated in detail. The method consists in proving first results for self-intersection local times of the ingredient processes: Wt, T't X0 and [Formula: see text], from which the results for Xt are derived. As a by-product, a class of non-finite tempered measures on ℝd whose Fourier transforms are functions is identified. The tools are mostly analytical.

DIVERGENCE RESULTS FOR SELF-INTERSECTION LOCAL TIMES OF GAUSSIAN ${\mathscr S}' ({\mathbb R}^d)$-PROCESSES

2001 ◽  
Vol 04 (04) ◽  
pp. 417-488 ◽  
Author(s):  
ANNA TALARCZYK
Keyword(s):  
Local Time ◽  
Necessary Conditions ◽  
Particle Systems ◽  
The Self ◽  
Local Times ◽  
Intersection Local Time ◽  
Convergence In Law ◽  
Stable Particle ◽  
Gaussian Formula ◽  
Intersection Local Times

For various types of Gaussian [Formula: see text]-processes we consider the case when the self-intersection local time (SILT) does not exist. We study the rate of divergence of the corresponding approximating processes obtaining, after suitable normalizations convergence in law to some [Formula: see text]-valued processes (not necessarily Gaussian). We also obtain some new necessary conditions for the existence of SILT. We give examples associated with fluctuation limits of α-stable particle systems.

scholarly journals Optimal Bounds for the Variance of Self-Intersection Local Times

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
George Deligiannidis ◽  
Sergey Utev
Keyword(s):  
Random Walk ◽  
Local Time ◽  
Simple Random Walk ◽  
The Self ◽  
The Other ◽  
Local Times ◽  
Intersection Local Time ◽  
Moment Conditions ◽  
Symmetric Random Walk ◽  
Optimal Bounds

For a Zd-valued random walk (Sn)n∈N0, let l(n,x) be its local time at the site x∈Zd. For α∈N, define the α-fold self-intersection local time as Ln(α)≔∑xl(n,x)α. Also let LnSRW(α) be the corresponding quantities for the simple random walk in Zd. Without imposing any moment conditions, we show that the variance of the self-intersection local time of any genuinely d-dimensional random walk is bounded above by the corresponding quantity for the simple symmetric random walk; that is, var(Ln(α))=O(var⁡(LnSRW(α))). In particular, for any genuinely d-dimensional random walk, with d≥4, we have var⁡(Ln(α))=O(n). On the other hand, in dimensions d≤3 we show that if the behaviour resembles that of simple random walk, in the sense that lim infn→∞var⁡Lnα/var⁡(LnSRW(α))>0, then the increments of the random walk must have zero mean and finite second moment.

scholarly journals Representations of hermite processes using local time of intersecting stationary stable regenerative sets

2020 ◽  
Vol 57 (4) ◽  
pp. 1234-1251
Author(s):  
Shuyang Bai
Keyword(s):  
Long Range ◽  
Local Time ◽  
Limit Theorems ◽  
Local Times ◽  
Long Range Dependence ◽  
Random Interval ◽  
Stationary Increments ◽  
Self Similar ◽  
Regenerative Sets

AbstractHermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener–Itô integrals, whose integrands involve the local time of intersecting stationary stable regenerative sets. The proof relies on an approximation of regenerative sets and local times based on a scheme of random interval covering.

scholarly journals Cluster observation of few-hour-scale evolution of structured plasma in the inner magnetosphere

2013 ◽  
Vol 31 (9) ◽  
pp. 1569-1578 ◽  
Author(s):  
M. Yamauchi ◽  
I. Dandouras ◽  
H. Rème ◽  
R. Lundin ◽  
L. M. Kistler
Keyword(s):  
Local Time ◽  
Trapped Ions ◽  
Low Energy ◽  
Local Times ◽  
Significant Enhancement ◽  
Occurrence Rate ◽  
Wide Energy Range ◽  
Inner Magnetosphere ◽  
Wide Energy ◽  
Cluster Ion

Abstract. Using Cluster Ion Spectrometry (CIS) data from the spacecraft-4 perigee traversals during the 2001–2006 period (nearly 500 traversals after removing those that are highly contaminated by radiation belt particles), we statistically examined the local time distribution of structured trapped ions at sub- to few-keV range as well as inbound–outbound differences of these ion signatures in intensities and energy–latitude dispersion directions. Since the Cluster orbit during this period was almost constant and approximately north–south symmetric at nearly constant local time near the perigee, inbound–outbound differences are attributed to temporal developments in a 1–2 h timescale. Three types of structured ions at sub- to few keV range that are commonly found in the inner magnetosphere are examined: – Energy–latitude dispersed structured ions at less than a few keV, – Short-lived dispersionless ion stripes at wide energy range extending 0.1–10 keV, – Short-lived low-energy ion bursts at less than a few hundred eV. The statistics revealed that the wedge-like dispersed ions are most often observed in the dawn sector (60% of traversals), and a large portion of them show significant enhancement during the traversals at all local times. The short-lived ion stripes are predominantly found near midnight, where most stripes are significantly enhanced during the traversals and are associated with substorm activities with geomagnetic AL < −300 nT. The low-energy bursts are observed at all local times and under all geomagnetic conditions, with moderate peak of the occurrence rate in the afternoon sector. A large portion of them again show significant enhancement or decay during the traversals.

Derivative of intersection local time of independent symmetric stable motions

2017 ◽  
Vol 121 ◽  
pp. 18-28 ◽  
Author(s):  
Litan Yan ◽  
Xianye Yu ◽  
Ruqing Chen
Keyword(s):  
Local Time ◽  
Intersection Local Time

scholarly journals New results on equatorial thermospheric winds and temperatures from Ethiopia, Africa

2017 ◽  
Vol 35 (2) ◽  
pp. 333-344 ◽  
Author(s):  
Fasil Tesema ◽  
Rafael Mesquita ◽  
John Meriwether ◽  
Baylie Damtie ◽  
Melessew Nigussie ◽  
...  
Keyword(s):  
Local Time ◽  
Zonal Wind ◽  
Meridional Wind ◽  
Local Times ◽  
Maximum Speed ◽  
Wind Speeds ◽  
Early Evening ◽  
Meridional Winds ◽  
Thermospheric Winds ◽  
Wind Surge

Abstract. Measurements of equatorial thermospheric winds, temperatures, and 630 nm relative intensities were obtained using an imaging Fabry–Perot interferometer (FPI), which was recently deployed at Bahir Dar University in Ethiopia (11.6° N, 37.4° E, 3.7° N magnetic). The results obtained in this study cover 6 months (53 nights of useable data) between November 2015 and April 2016. The monthly-averaged values, which include local winter and equinox seasons, show the magnitude of the maximum monthly-averaged zonal wind is typically within the range of 70 to 90 ms−1 and is eastward between 19:00 and 21:00 LT. Compared to prior studies of the equatorial thermospheric wind for this local time period, the magnitude is considerably weaker as compared to the maximum zonal wind speed observed in the Peruvian sector but comparable to Brazilian FPI results. During the early evening, the meridional wind speeds are 30 to 50 ms−1 poleward during the winter months and 10 to 25 ms−1 equatorward in the equinox months. The direction of the poleward wind during the winter months is believed to be mainly caused by the existence of the interhemispheric wind flow from the summer to winter hemispheres. An equatorial wind surge is observed later in the evening and is shifted to later local times during the winter months and to earlier local times during the equinox months. Significant night-to-night variations are also observed in the maximum speed of both zonal and meridional winds. The temperature observations show the midnight temperature maximum (MTM) to be generally present between 00:30 and 02:00 LT. The amplitude of the MTM was  ∼  110 K in January 2016 with values smaller than this in the other months. The local time difference between the appearance of the MTM and a pre-midnight equatorial wind was generally 60 to 180 min. A meridional wind reversal was also observed after the appearance of the MTM (after 02:00 LT). Climatological models, HWM14 and MSIS-00, were compared to the observations and the HWM14 model generally predicted the zonal wind observations well with the exception of higher model values by 25 ms−1 in the winter months. The HWM14 model meridional wind showed generally good agreement with the observations. Finally, the MSIS-00 model overestimated the temperature by 50 to 75 K during the early evening hours of local winter months. Otherwise, the agreement was generally good, although, in line with prior studies, the model failed to reproduce the MTM peak for any of the 6 months compared with the FPI data.

scholarly journals Condition for intersection occupation measure to be absolutely continuous

2020 ◽  
Vol 72 (9) ◽  
pp. 1304-1312
Author(s):  
X. Chen
Keyword(s):  
Stochastic Processes ◽  
Lebesgue Measure ◽  
Local Time ◽  
Minimal Condition ◽  
Occupation Measure ◽  
Absolutely Continuous ◽  
Intersection Local Time ◽  
Stationary Increments

UDC 519.21 Given the i.i.d. -valued stochastic processes with the stationary increments, a minimal condition is provided for the occupation measure to be absolutely continuous with respect to the Lebesgue measure on An isometry identity related to the resulting density (known as intersection local time) is also established.

scholarly journals Temperature decadal trends, and their relation to diurnal variations in the lower thermosphere, stratosphere, and mesosphere, based on measurements from SABER on TIMED

2021 ◽  
Vol 39 (2) ◽  
pp. 327-339
Author(s):  
Frank T. Huang ◽  
Hans G. Mayr
Keyword(s):  
Local Time ◽  
Lower Thermosphere ◽  
3D Models ◽  
Diurnal Variations ◽  
Local Times ◽  
Temperature Trends ◽  
Microwave Sounding Unit ◽  
Lidar Measurements ◽  
Microwave Sounding ◽  
Thermal Tides

Abstract. We have derived the behavior of decadal temperature trends over the 24 h of local time, based on zonal averages of SABER data, for the years 2012 to 2014, from 20 to 100 km, within 48∘ of the Equator. Similar results have not been available previously. We find that the temperature trends, based on zonal mean measurements at a fixed local time, can be different from those based on measurements made at a different fixed local time. The trends can vary significantly in local time, even from hour to hour. This agrees with some findings based on nighttime lidar measurements. This knowledge is relevant because the large majority of temperature measurements, especially in the stratosphere, are made by instruments on sun-synchronous operational satellites which measure at only one or two fixed local times, for the duration of their missions. In these cases, the zonal mean trends derived from various satellite data are tied to the specific local times at which each instrument samples the data, and the trends are then also biased by the local time. Consequently, care is needed in comparing trends based on various measurements with each other, unless the data are all measured at the same local time. Similar caution is needed when comparing with models, since the zonal means from 3D models reflect averages over both longitude and the 24 h of local time. Consideration is also needed in merging data from various sources to produce generic, continuous, longer-term records. Diurnal variations of temperature themselves, in the form of thermal tides, are well known and are due to absorption of solar radiation. We find that at least part of the reason that temperature trends are different for different local times is that the amplitudes and phases of the tides themselves follow trends over the same time span of the data. Many of the past efforts have focused on the temperature values with local time when merging data from various sources and on the effect of unintended satellite orbital drifts, which result in drifting local times at which the temperatures are measured. However, the effect of local time on trends has not been well researched. We also derive estimates of trends by simulating the drift of local time due to drifting orbits. Our comparisons with results found by others (Advanced Microwave Sounding Unit, AMSU; lidar) are favorable and informative. They may explain, at least in part, the bridge between results based on daytime AMSU data and nighttime lidar measurements. However, these examples do not form a pattern, and more comparisons and study are needed.

Sign in / Sign up

Export Citation Format

Share Document