Functional calculus of Laplace transform type on non-doubling parabolic manifolds with ends

2021 ◽  
Vol -1 (-1) ◽  
Author(s):  
Hong Chuong DOAN
Keyword(s):  
Laplace Transform ◽  
Functional Calculus

Functional calculus via Laplace transform and equations with infinitely many derivatives

2010 ◽  
Vol 51 (10) ◽  
pp. 103512 ◽  
Author(s):  
P. Górka ◽  
H. Prado ◽  
E. G. Reyes
Keyword(s):  
Laplace Transform ◽  
Functional Calculus

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Properties of the Local Functional Calculus

2002 ◽  
Vol 102 (2) ◽  
pp. 215-225
Author(s):  
Teresa Bermύdez ◽  
Manuel González ◽  
Antonio Martinόn
Keyword(s):  
Functional Calculus ◽  
Local Functional

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

Measuring the error of dynamic hedging: a Laplace transform approach

2009 ◽  
Vol 13 (2) ◽  
pp. 47-72 ◽  
Author(s):  
Flavio Angelini ◽  
Stefano Herzel
Keyword(s):  
Laplace Transform ◽  
Dynamic Hedging
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