Soft local times and decoupling of random interlacements

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.

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An Embedding of Compensated Compound Poisson Processes with Applications to Local Times

The Annals of Probability ◽

10.1214/aop/1176989408 ◽

1993 ◽

Vol 21 (1) ◽

pp. 340-361 ◽

Cited By ~ 6

Author(s):

Davar Khoshnevisan

Keyword(s):

Poisson Processes ◽

Local Times ◽

Compound Poisson ◽

Compound Poisson Processes

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

Atmospheric Chemistry and Physics ◽

10.5194/acp-13-7813-2013 ◽

2013 ◽

Vol 13 (15) ◽

pp. 7813-7824 ◽

Cited By ~ 4

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.

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

Advances in Applied Probability ◽

10.1017/s0001867800002639 ◽

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.

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