scholarly journals A change of variable for Dahlberg-Kenig-Pipher operators.

2021 ◽  
Author(s):  
Joseph Feneuil
Keyword(s):  
Change Of Variable

Improved correlation dimension estimates through change of variable

1992 ◽  
Vol 163 (4) ◽  
pp. 269-274 ◽  
Author(s):  
M. Lefranc ◽  
D. Hennequin ◽  
P. Glorieux
Keyword(s):  
Correlation Dimension ◽  
Change Of Variable

scholarly journals r-Dependence in Two-Point Orientation Coherence Functions

2000 ◽  
Vol 34 (4) ◽  
pp. 233-241
Author(s):  
Peter R. Morris
Keyword(s):  
Correlation Function ◽  
Weight Function ◽  
Bessel Functions ◽  
Unit Weight ◽  
Experimental Procedure ◽  
Change Of Variable

Functions are derived, which are orthonormal on the range r=0, 1, with weight function corresponding to the distribution of r in a typical experimental procedure for measurement of the two-point orientation–coherence (or orientation–correlation) function. These are obtained by making an appropriate change of variable in spherical Bessel functions, orthonormal on the range r=0, 1, with unit weight function. The effects of weight function and change of variable on the functions are considered.

ON THE VALUATION OF DERIVATIVES WITH SNAPSHOT RESET FEATURES

2008 ◽  
Vol 11 (08) ◽  
pp. 905-941 ◽  
Author(s):  
ERIC C. K. YU ◽  
WILLIAM T. SHAW
Keyword(s):  
Convertible Bonds ◽  
Convertible Bond ◽  
Put Options ◽  
Risk Characteristics ◽  
Black Scholes ◽  
Barrier Type ◽  
Simple Change ◽  
Discontinuous Nature ◽  
Change Of Variable ◽  
Digital Options

We propose a general approach that requires only a simple change of variable that keeps the valuation of call and put options (convertible bonds) with strike (conversion) price resets two-dimensional in the classical Black–Scholes setting. A link between reset derivatives, compound options and "discrete barrier" type options, when there is one reset is then discussed, from which we analyze the risk characteristics of reset derivatives, which can be significantly different from their vanilla counterparts. We also generalize the prototype reset structure and show that the delta and gamma of a convertible bond with reset can both be negative. Finally, we show that the "waviness" property found in the delta and gamma of some reset derivatives is due to the discontinuous nature of the reset structure, which is closely linked to digital options.

Integral equations for compound distribution functions

1996 ◽  
Vol 33 (2) ◽  
pp. 388-399 ◽  
Author(s):  
Christian Max Møller
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Building Blocks ◽  
Distribution Functions ◽  
Jump Processes ◽  
Marked Point Processes ◽  
Martingale Theory ◽  
Compound Distribution ◽  
Change Of Variable ◽  
Fixed Period

The aim of the present paper is to introduce some techniques, based on the change of variable formula for processes of finite variation, for establishing (integro) differential equations for evaluating the distribution of jump processes for a fixed period of time. This is of interest in insurance mathematics for evaluating the distribution of the total amount of claims occurred over some period of time, and attention will be given to such issues. Firstly we will study some techniques when the process has independent increments, and then a more refined martingale technique is discussed. The building blocks are delivered by the theory of marked point processes and associated martingale theory. A simple numerical example is given.

A Class of Singular Volterra-Fredholm Type Difference Inequality in Engineering

2014 ◽  
Vol 571-572 ◽  
pp. 132-138
Author(s):  
Wu Sheng Wang ◽  
Chun Miao Huang
Keyword(s):  
Beta Function ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Jensen Inequality ◽  
Fredholm Type ◽  
Difference Inequality ◽  
Amplification Method ◽  
Change Of Variable ◽  
Explicit Bounds ◽  
The Mean

In this paper, we discuss a class of new weakly singular Volterra-Fredholm difference inequality, which is solved using change of variable, discrete Jensen inequality, Beta function, the mean-value theorem for integrals and amplification method, and explicit bounds for the unknown functions is given clearly. The derived results can be applied in the study of fractional difference equations in engineering.

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