Definition of the Stochastic Integral

2013 ◽  
pp. 23-56
Author(s):  
K. L. Chung ◽  
R. J. Williams
Keyword(s):  
Stochastic Integral ◽  
Definition Of

Exponential formulae in quantum stochastic calculus

1996 ◽  
Vol 126 (2) ◽  
pp. 375-389 ◽  
Author(s):  
A. S. Holevo
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Degrees Of Freedom ◽  
Stochastic Integral ◽  
Stochastic Calculus ◽  
Exponential Equation ◽  
Quantum Stochastic Calculus ◽  
Rigorous Definition ◽  
Definition Of

The rigorous definition of time-ordered exponentials, solving quantum linear stochastic differential equations, is extended to Boson and Fermion stochastic calculi with infinitely many degrees of freedom. The relation to the classicalmultiplicative stochastic integral, solving the Doleans exponential equation, is discussed.

A Practical Approach to Fractional Stochastic Dynamics

2013 ◽  
Vol 8 (3) ◽  
Author(s):  
Tran Hung Thao
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Existence And Uniqueness ◽  
Stochastic Dynamics ◽  
Stochastic Integral ◽  
Approximation Approach ◽  
Fractional Stochastic Differential Equations ◽  
Definition Of ◽  
Simple Definition

In this note we present some results on stochastic dynamics with respect to a fractional Brownian motion from a L2-approximation approach. A new and simple definition of fractional stochastic integral is introduced and a theorem of existence and uniqueness for fractional stochastic differential equations is established.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Sign in / Sign up

Export Citation Format

Share Document