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.

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

2011 ◽  
Vol 90 (104) ◽  
pp. 65-84 ◽  
Author(s):  
Tijana Levajkovic ◽  
Dora Selesi
Keyword(s):  
Hilbert Space ◽  
White Noise ◽  
Orthogonal Basis ◽  
Chaos Expansion ◽  
Charlier Polynomials ◽  
Malliavin Derivative ◽  
Second Moments ◽  
Skorokhod Integral ◽  
Relationship Of ◽  
The Relationship

We consider Gaussian, Poissonian, fractional Gaussian and fractional Poissonian white noise spaces, all represented through the corresponding orthogonal basis of the Hilbert space of random variables with finite second moments, given by the Hermite and the Charlier polynomials. There exist unitary mappings between the Gaussian and Poissonian white noise spaces. We investigate the relationship of the Malliavin derivative, the Skorokhod integral, the Ornstein-Uhlenbeck operator and their fractional counterparts on a general white noise space.

A chaos expansion approach for the pricing of contingent claims

2015 ◽  
Vol 18 (3) ◽  
pp. 27-58 ◽  
Author(s):  
Hideharu Funahashi ◽  
Masaaki Kijima
Keyword(s):  
Contingent Claims ◽  
Chaos Expansion
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