Exponential Moments of Solutions for Nonlinear Equations with Catalytic Noise and Large Deviation

2001 ◽  
pp. 101-117
Author(s):  
Isamu Dôku
Keyword(s):  
Nonlinear Equations ◽  
Large Deviation ◽  
Exponential Moments

scholarly journals The existence of quermass-interaction processes for nonlocally stable interaction and nonbounded convex grains

2009 ◽  
Vol 41 (03) ◽  
pp. 664-681 ◽  
Author(s):  
David Dereudre
Keyword(s):  
Linear Combination ◽  
Large Deviation ◽  
General Setting ◽  
Infinite Volume ◽  
Minkowski Functionals ◽  
Interaction Processes ◽  
Exponential Moments

We prove the existence of infinite-volume quermass-interaction processes in a general setting of nonlocally stable interaction and nonbounded convex grains. No condition on the parameters of the linear combination of the Minkowski functionals is assumed. The only condition is that the square of the random radius of the grain admits exponential moments for all orders. Our methods are based on entropy and large deviation tools.

scholarly journals Exact Lower Bounds on the Exponential Moments of Truncated Random Variables

2011 ◽  
Vol 48 (02) ◽  
pp. 547-560 ◽  
Author(s):  
Iosif Pinelis
Keyword(s):  
Option Pricing ◽  
Lower Bounds ◽  
Large Deviation ◽  
Asymptotic Properties ◽  
Random Variables ◽  
Random Variable ◽  
Exponential Moments ◽  
Comparative Advantages ◽  
Large Deviation Probabilities

Exact lower bounds on the exponential moments of min(y,X) andX1{X<y} are provided given the first two moments of a random variableX. These bounds are useful in work on large deviation probabilities and nonuniform Berry-Esseen bounds, when the Cramér tilt transform may be employed. Asymptotic properties of these lower bounds are presented. Comparative advantages of the so-called Winsorization min(y,X) over the truncationX1{X<y} are demonstrated. An application to option pricing is given.

scholarly journals Exact Lower Bounds on the Exponential Moments of Truncated Random Variables

2011 ◽  
Vol 48 (2) ◽  
pp. 547-560 ◽  
Author(s):  
Iosif Pinelis
Keyword(s):  
Option Pricing ◽  
Lower Bounds ◽  
Large Deviation ◽  
Asymptotic Properties ◽  
Random Variables ◽  
Random Variable ◽  
Exponential Moments ◽  
Comparative Advantages ◽  
Large Deviation Probabilities

Exact lower bounds on the exponential moments of min(y, X) and X1{X < y} are provided given the first two moments of a random variable X. These bounds are useful in work on large deviation probabilities and nonuniform Berry-Esseen bounds, when the Cramér tilt transform may be employed. Asymptotic properties of these lower bounds are presented. Comparative advantages of the so-called Winsorization min(y, X) over the truncation X1{X < y} are demonstrated. An application to option pricing is given.

scholarly journals The existence of quermass-interaction processes for nonlocally stable interaction and nonbounded convex grains

2009 ◽  
Vol 41 (3) ◽  
pp. 664-681 ◽  
Author(s):  
David Dereudre
Keyword(s):  
Linear Combination ◽  
Large Deviation ◽  
General Setting ◽  
Infinite Volume ◽  
Minkowski Functionals ◽  
Interaction Processes ◽  
Exponential Moments

We prove the existence of infinite-volume quermass-interaction processes in a general setting of nonlocally stable interaction and nonbounded convex grains. No condition on the parameters of the linear combination of the Minkowski functionals is assumed. The only condition is that the square of the random radius of the grain admits exponential moments for all orders. Our methods are based on entropy and large deviation tools.

Solving System of Nonlinear Equations using Genetic Algorithm

2019 ◽  
Vol 10 (4) ◽  
pp. 877-886 ◽  
Author(s):  
Chhavi Mangla ◽  
Musheer Ahmad ◽  
Moin Uddin
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations
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