scholarly journals Rice formula for processes with jumps and applications

Extremes ◽  
2014 ◽  
Vol 18 (1) ◽  
pp. 15-35 ◽  
Author(s):  
Federico Dalmao ◽  
Ernesto Mordecki
Keyword(s):  
Rice Formula

scholarly journals Level Sets of Random Fields and Applications: Specular Points and Wave Crests

2010 ◽  
Vol 2010 ◽  
pp. 1-22
Author(s):  
Esteban Flores ◽  
José R. León R
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Random Fields ◽  
Level Sets ◽  
Two Dimensions ◽  
Level Curve ◽  
Curvilinear Integral ◽  
The Waves ◽  
Rice Formula

We apply Rice's multidimensional formulas, in a mathematically rigorous way, to several problems which appear in random sea modeling. As a first example, the probability density function of the velocity of the specular points is obtained in one or two dimensions as well as the expectation of the number of specular points in two dimensions. We also consider, based on a multidimensional Rice formula, a curvilinear integral with respect to the level curve. It follows that its expected value allows defining the Palm distribution of the angle of the normal of the curve that defines the waves crest. Finally, we give a new proof of a general multidimensional Rice formula, valid for all levels, for a stationary and smooth enough random fields X:ℝd→ℝj(d>j).

scholarly journals q-identities of Fu and Lascoux proved by theq-rice formula

2004 ◽  
Vol 27 (4) ◽  
pp. 391-395 ◽  
Author(s):  
Helmut Prodinger
Keyword(s):  
Rice Formula

scholarly journals On a General $q$-Identity

10.37236/3962 ◽  
2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Aimin Xu
Keyword(s):  
Harmonic Numbers ◽  
Special Cases ◽  
Generalized Harmonic Numbers ◽  
Rice Formula

In this paper, by means of the $q$-Rice formula we obtain a general $q$-identity which is a unified generalization of three kinds of identities. Some known results are special cases of ours. Meanwhile, some identities on $q$-generalized harmonic numbers are also derived.

Some applications of theq-Rice formula

2001 ◽  
Vol 19 (3-4) ◽  
pp. 552-557 ◽  
Author(s):  
Helmut Prodinger
Keyword(s):  
Rice Formula
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