Normal-ordered white noise differential equations. II: Regularity properties of solutions

1999 ◽  
pp. 157-174 ◽  
Keyword(s):  
Differential Equations ◽  
White Noise ◽  
Regularity Properties

QUANTUM STOCHASTIC ANALYSIS VIA WHITE NOISE OPERATORS IN WEIGHTED FOCK SPACE

2002 ◽  
Vol 14 (03) ◽  
pp. 241-272 ◽  
Author(s):  
DONG MYUNG CHUNG ◽  
UN CIG JI ◽  
NOBUAKI OBATA
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
White Noise ◽  
Fock Space ◽  
Existence Of A Solution ◽  
Quantum Stochastic Differential Equation ◽  
Unique Existence ◽  
Regularity Properties ◽  
Weighted Fock Space ◽  
White Noises

White noise theory allows to formulate quantum white noises explicitly as elemental quantum stochastic processes. A traditional quantum stochastic differential equation of Itô type is brought into a normal-ordered white noise differential equation driven by lower powers of quantum white noises. The class of normal-ordered white noise differential equations covers quantum stochastic differential equations with highly singular noises such as higher powers or higher order derivatives of quantum white noises, which are far beyond the traditional Itô theory. For a general normal-ordered white noise differential equation unique existence of a solution is proved in the sense of white noise distribution. Its regularity properties are investigated by means of weighted Fock spaces interpolating spaces of white noise distributions and associated characterization theorems for S-transform and for operator symbols.

scholarly journals Some Applications of Lévy Processes to Stochastic Investment Models for Actuarial Use

1998 ◽  
Vol 28 (1) ◽  
pp. 77-93 ◽  
Author(s):  
Terence Chan
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Differential Equations ◽  
White Noise ◽  
Stochastic Differential Equations ◽  
Continuous Time ◽  
Investment Model ◽  
Stable Processes ◽  
Gamma Processes ◽  
Investment Models

AbstractThis paper presents a continuous time version of a stochastic investment model originally due to Wilkie. The model is constructed via stochastic differential equations. Explicit distributions are obtained in the case where the SDEs are driven by Brownian motion, which is the continuous time analogue of the time series with white noise residuals considered by Wilkie. In addition, the cases where the driving “noise” are stable processes and Gamma processes are considered.

scholarly journals On Some regularity properties for solutions of nonlinear parabolic differential equations

1992 ◽  
Vol 128 ◽  
pp. 49-63 ◽  
Author(s):  
Haruo Nagase
Keyword(s):  
Differential Equations ◽  
Bounded Domain ◽  
Open Interval ◽  
Function Spaces ◽  
Parabolic Differential Equations ◽  
Regularity Properties ◽  
Nonlinear Parabolic ◽  
Class C

Let G be a bounded domain in Rn with coordinates x = (x1,…,xn) and let its boundary S be of class C2. We assume that the usual function spaces Lq(G), Wl, q(G) and are known. We write the norm of Lq(G) by | |q and the adjoint number of q by q*, i.e., q* = q/(q —1).For any positive number T we denote the open interval (0,T) by I, the cylinder G X I in Rn+1 by Q and the norm of Lq(Q) by ‖ ‖q.

scholarly journals ON THE UNITARITY OF STOCHASTIC EVOLUTIONS DRIVEN BY THE SQUARE OF WHITE NOISE

2001 ◽  
Vol 04 (04) ◽  
pp. 579-588 ◽  
Author(s):  
LUIGI ACCARDI ◽  
ANDREAS BOUKAS ◽  
HUI-HSUNG KUO
Keyword(s):  
Differential Equations ◽  
White Noise ◽  
Stochastic Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

Using the closed Itô's table for the renormalized square of white noise, recently obtained by Accardi, Hida, and Kuo in Ref. 4, we consider the problem of providing necessary and sufficient conditions for the unitarity of the solutions of a certain type of quantum stochastic differential equations.

Sign in / Sign up

Export Citation Format

Share Document