scholarly journals Chaos expansion methods for stochastic differential equations involving the Malliavin derivative, Part II

2011 ◽  
Vol 90 (104) ◽  
pp. 85-98 ◽  
Author(s):  
Tijana Levajkovic ◽  
Dora Selesi
Keyword(s):  
Differential Equations ◽  
White Noise ◽  
Stochastic Differential Equations ◽  
Chaos Expansion ◽  
Malliavin Derivative ◽  
White Noise Space

We solve stochastic differential equations involving the Malliavin derivative and the fractional Malliavin derivative by means of a chaos expansion on a general white noise space (Gaussian, Poissonian, fractional Gaussian and fractional Poissonian white noise space). There exist unitary mappings between the Gaussian and Poissonian white noise spaces, which can be applied in solving SDEs.

Stochastic Differential Equations in White Noise Space

1998 ◽  
Vol 01 (04) ◽  
pp. 611-632 ◽  
Author(s):  
H.-H. Kuo ◽  
J. Xiong
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
White Noise ◽  
Stochastic Differential Equations ◽  
Generalized Functions ◽  
Two Dimensional ◽  
Stochastic Fluctuation ◽  
Infinite Dimensional ◽  
Distribution Laws ◽  
White Noise Space

We study infinite dimensional stochastic differential equations taking values in a white noise space. We show that under certain assumptions the distribution laws of the solution of such an equation induce generalized functions. The white noise integral equation satisfied by these generalized functions is derived. We apply the results to study the stochastic fluctuation of a two-dimensional neuron.

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 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.

Free white noise flows

2017 ◽  
Vol 20 (03) ◽  
pp. 1750014 ◽  
Author(s):  
Luigi Accardi ◽  
Wided Ayed
Keyword(s):  
Differential Equations ◽  
White Noise ◽  
Stochastic Differential Equations ◽  
Microscopic Structure ◽  
Stochastic Flows ◽  
Heisenberg Equations

We extend to free white noise Heisenberg equations the proof of the equivalence between (non-Hamiltonian) stochastic differential equations and Hamiltonian white noise equations. This gives in particular, the microscopic structure of the maps defining free white noise stochastic flows in terms of the free white noise derivations defining them.

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