scholarly journals A White Noise Approach to Stochastic Integration with Respect to the Rosenblatt Process

2015 ◽  
Vol 43 (4) ◽  
pp. 547-591 ◽  
Author(s):  
Benjamin Arras
Keyword(s):  
White Noise ◽  
Stochastic Integration ◽  
Rosenblatt Process

scholarly journals White noise approach to stochastic integration

1988 ◽  
Vol 24 (2) ◽  
pp. 218-236 ◽  
Author(s):  
Hui-Hsiung Kuo ◽  
Andrzej Russek
Keyword(s):  
White Noise ◽  
Stochastic Integration

AN EXTENDED STOCHASTIC INTEGRAL AND A WICK CALCULUS ON PARAMETRIZED KONDRATIEV-TYPE SPACES OF MEIXNER WHITE NOISE

2008 ◽  
Vol 11 (04) ◽  
pp. 541-564 ◽  
Author(s):  
N. A. KACHANOVSKY
Keyword(s):  
White Noise ◽  
Stochastic Equation ◽  
Stochastic Integral ◽  
Holomorphic Functions ◽  
Generalized Functions ◽  
Wick Product ◽  
Stochastic Integration ◽  
Type Spaces ◽  
Wick Calculus

Using a general approach that covers the cases of Gaussian, Poissonian, Gamma, Pascal and Meixner measures, we consider an extended stochastic integral and construct elements of a Wick calculus on parametrized Kondratiev-type spaces of generalized functions; consider the interconnection between the extended stochastic integration and the Wick calculus; and give an example of a stochastic equation with a Wick-type nonlinearity. The main results consist of studying the properties of the extended (Skorohod) stichastic integral subject to the particular spaces under consideration; and of studying the properties of a Wick product and Wick versions of holomorphic functions on the parametrized Kondratiev-type spaces. These results are necessary, in particular, in order to describe properties of solutions of normally ordered white noise equations in the "Meixner analysis".

scholarly journals White Noise Approach to stochastic integration

2005 ◽  
Vol 13 (4) ◽  
Author(s):  
Luigi Accardi ◽  
Wided Ayed ◽  
Habib Ouerdiane
Keyword(s):  
White Noise ◽  
Stochastic Integration

Stochastic integration via white noise analysis

1997 ◽  
Vol 30 (1) ◽  
pp. 317-328 ◽  
Author(s):  
Hui-Hsiung Kuo
Keyword(s):  
White Noise ◽  
Noise Analysis ◽  
Stochastic Integration ◽  
White Noise Analysis

scholarly journals FRACTIONAL WHITE NOISE CALCULUS AND APPLICATIONS TO FINANCE

2003 ◽  
Vol 06 (01) ◽  
pp. 1-32 ◽  
Author(s):  
YAOZHONG HU ◽  
BERNT ØKSENDAL
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Fractional Brownian Motion ◽  
Standard Brownian Motion ◽  
Stochastic Integration ◽  
European Option ◽  
No Arbitrage ◽  
Black Scholes ◽  
White Noise Calculus ◽  
Replicating Portfolio

The purpose of this paper is to develop a fractional white noise calculus and to apply this to markets modeled by (Wick–) Itô type of stochastic differential equations driven by fractional Brownian motion BH(t); 1/2 < H < 1. We show that if we use an Itô type of stochastic integration with respect to BH(t) (as developed in Ref. 8), then the corresponding Itô fractional Black–Scholes market has no arbitrage, contrary to the situation when the pathwise integration is used. Moreover, we prove that our Itô fractional Black–Scholes market is complete and we compute explicitly the price and replicating portfolio of a European option in this market. The results are compared to the classical results based on standard Brownian motion B(t).

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