Simple derivation and closed-form frequency-domain design of wideband length-8 interpolation kernel

2017 ◽  
Vol 137 ◽  
pp. 135-148
Author(s):  
Tian-Bo Deng
Keyword(s):  
Closed Form ◽  
Frequency Domain ◽  
Simple Derivation

A simple derivation of Cordell’s stripping filter

Geophysics ◽  
1994 ◽  
Vol 59 (3) ◽  
pp. 488-490 ◽  
Author(s):  
Adebayo Aina
Keyword(s):  
Frequency Domain ◽  
Potential Field ◽  
Simple Derivation ◽  
Regional Background ◽  
Deep Source ◽  
Local Anomalies

The presence of a strong regional (deep source) anomaly often makes the identification of local (shallow source) anomalies difficult. It may become necessary to either separate the regional and the residual, or carry out an operation on the observed map that enhances the local anomalies at the expense of the regional background. The problem of separation of deep and shallow‐source potential field anomalies is one of the oldest problems in geophysics. Various authors (Griffin, 1949; Nettleton, 1954; Abdelrahman et. al., 1985, for example) have presented details and schemes for separating residual and background anomalies. More recently, Cordell (1985) through Green’s equivalent stratum theorem obtained a filter in the frequency domain that may be used for separating shallow and deep‐source potential field anomalies.

scholarly journals Some applications of occupation times of Brownian motion with drift in mathematical finance

1999 ◽  
Vol 3 (1) ◽  
pp. 63-73 ◽  
Author(s):  
Andreas Pechtl
Keyword(s):  
Brownian Motion ◽  
Closed Form ◽  
Mathematical Finance ◽  
European Options ◽  
Options Markets ◽  
Occupation Times ◽  
Simple Derivation ◽  
Brownian Motion With Drift ◽  
Derivative Instruments ◽  
Path Dependent

In the last few years new types of path-dependent options called corridor options or range options have become well-known derivative instruments in European options markets. Since the payout profiles of those options are based on occupation times of the underlying security the purpose of this paper is to provide closed form pricing formulae of Black & Scholes type for some significant representatives. Alternatively we demonstrate in this paper a relatively simple derivation of the Black & Scholes price for a single corridor option – based on a static portfolio representation – which does not make use of the distribution of occupation times (of Brownian motion). However, knowledge of occupation times' distributions is a more powerful tool.

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