The Existence and Regularity of Semimartingale Local Times

2013 ◽  
pp. 13-28
Author(s):  
Ju-Yi Yen ◽  
Marc Yor
Keyword(s):  
Local Times

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 The roles of vertical advection and eddy diffusion in the equatorial mesospheric semi-annual oscillation (MSAO)

2013 ◽  
Vol 13 (15) ◽  
pp. 7813-7824 ◽  
Author(s):  
R. L. Gattinger ◽  
E. Kyrölä ◽  
C. D. Boone ◽  
W. F. J. Evans ◽  
K. A. Walker ◽  
...  
Keyword(s):  
Driving Forces ◽  
Eddy Diffusion ◽  
Equatorial Region ◽  
Local Times ◽  
Model Simulations ◽  
Vertical Advection ◽  
Diffusion Rates ◽  
D Model ◽  
Vertical Eddy

Abstract. Observations of the mesospheric semi-annual oscillation (MSAO) in the equatorial region have been reported dating back several decades. Seasonal variations in both species densities and airglow emissions are well documented. The extensive observations available offer an excellent case study for comparison with model simulations. A broad range of MSAO measurements is summarised with emphasis on the 80–100 km region. The objective here is not to address directly the complicated driving forces of the MSAO, but rather to employ a combination of observations and model simulations to estimate the limits of some of the underlying dynamical processes. Photochemical model simulations are included for near-equinox and near-solstice conditions, the two times with notable differences in the observed MSAO parameters. Diurnal tides are incorporated in the model to facilitate comparisons of observations made at different local times. The roles of water vapour as the "driver" species and ozone as the "response" species are examined to test for consistency between the model results and observations. The simulations suggest the interactions between vertical eddy diffusion and background vertical advection play a significant role in the MSAO phenomenon. Further, the simulations imply there are rigid limits on vertical advection rates and eddy diffusion rates. For August at the Equator, 90 km altitude, the derived eddy diffusion rate is approximately 1 × 106 cm2 s−1 and the vertical advection is upwards at 0.8 cm s−1. For April the corresponding values are 4 × 105 cm2 s−1 and 0.1 cm s−1. These results from the current 1-D model simulations will need to be verified by a full 3-D simulation. Exactly how vertical advection and eddy diffusion are related to gravity wave momentum as discussed by Dunkerton (1982) three decades ago remains to be addressed.

scholarly journals Boundary behavior and product-form stationary distributions of jump diffusions in the orthant with state-dependent reflections

2008 ◽  
Vol 40 (02) ◽  
pp. 529-547
Author(s):  
Francisco J. Piera ◽  
Ravi R. Mazumdar ◽  
Fabrice M. Guillemin
Keyword(s):  
Random Fields ◽  
Diffusion Coefficients ◽  
Boundary Behavior ◽  
Stationary Regime ◽  
Product Form ◽  
Local Times ◽  
Nonnegative Orthant ◽  
State Dependent ◽  
The Times ◽  
And Diffusion

In this paper we consider reflected diffusions with positive and negative jumps, constrained to lie in the nonnegative orthant of ℝ n . We allow for the drift and diffusion coefficients, as well as for the directions of reflection, to be random fields over time and space. We provide a boundary behavior characterization, generalizing known results in the nonrandom coefficients and constant directions of the reflection case. In particular, the regulator processes are related to semimartingale local times at the boundaries, and they are shown not to charge the times the process expends at the intersection of boundary faces. Using the boundary results, we extend the conditions for product-form distributions in the stationary regime to the case when the drift and diffusion coefficients, as well as the directions of reflection, are random fields over space.

scholarly journals Derivatives of local times for some Gaussian fields II

2021 ◽  
Vol 172 ◽  
pp. 109063
Author(s):  
Minhao Hong ◽  
Fangjun Xu
Keyword(s):  
Local Times ◽  
Gaussian Fields ◽  
Derivatives Of

Sulfuric acid vapor and sulfur dioxide in the atmosphere of Venus as observed by the Venus Express Radio Science Experiment VeRa

2021 ◽  
Author(s):  
Janusz Oschlisniok ◽  
Bernd Häusler ◽  
Martin Pätzold ◽  
Silvia Tellmann ◽  
Michael Bird
Keyword(s):  
Sulfuric Acid ◽  
Transport Model ◽  
Lower Atmosphere ◽  
Local Times ◽  
Acid Vapor ◽  
Radio Science ◽  
X Band ◽  
Wide Range ◽  
Venus Express ◽  
Atmosphere Of Venus

<p>The main cloud deck within Venus' atmosphere, which covers the entire planet between approx. 50 and 70 km altitude, is believed to consist mostly of liquid sulfuric acid. The temperature below the main clouds is high enough to evaporate the H2SO4 droplets into gaseous sulfuric acid forming a haze layer which extends to altitudes as deep as 35 km. Gaseous sulfuric acid in Venus’ lower atmosphere is responsible for a strong absorption of radio waves as seen in Mariner, Pioneer Venus, Magellan and Venera radio science observations. Radio wave absorption measurements can be used to derive the amount of H2SO4 in Venus’ atmosphere. The radio science experiment VeRa onboard Venus Express probed the atmosphere of Venus between 2006 and 2014 with radio signals at 13 cm (S-band) and 3.6 cm (X-band) wavelengths. The orbit of the Venus Express spacecraft allowed to sound the atmosphere over a wide range of latitudes and local times providing a global picture of the sulfuric acid vapor distribution. We present the global H2SO4(g) distribution derived from the X-band radio signal attenuation for the time of the entire Venus Express mission. The observation is compared with results obtained from a 2-D transport model. The VeRa observations were additionally used to estimate the abundance of SO2 near the cloud bottom. The global distribution of SO2 at these altitudes is presented and compared with results obtained from other experiments. Eight years of VEX observation allow to study the long-term evolution of H2SO4 and SO2. The latter is presented for the northern polar region.</p>

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