Journal ArticleDOI
Forward, backward and symmetric stochastic integration
Francesco Russo,Pierre Vallois +1 more
Abstract:
We define three types of non causal stochastic integrals: forward, backward and symmetric. Our approach consists in approximating the integrator. Two optics are considered: the first one is based on traditional usual stochastic calculus and the second one on Wiener distributions.read more
Citations
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Journal ArticleDOI
Integration with respect to fractal functions and stochastic calculus. I
TL;DR: In this paper, the classical Lebesgue-Stieltjes integral is extended to a large class of integrands f and integrators g of unbounded variation, using composition formulas and integration-by-part rules for fractional integrals and Weyl derivatives.
Journal ArticleDOI
Stochastic integration with respect to fractional brownian motion
TL;DR: For every value of the Hurst index H ∈ (0, 1) as discussed by the authors, a stochastic integral with respect to fractional Brownian motion of index H is defined.
Journal ArticleDOI
Stochastic integration with respect to the fractional Brownian motion
Elisa Alòs,David Nualart +1 more
TL;DR: In this paper, a stochastic calculus for fractional Brownian motion with Hurst parameter H > 1/2 was developed using the techniques of the Malliavin calculus, and the authors established estimates in L p, maximal inequalities and a continuity criterion for the Stochastic integral.
Arbitrage with fractional Brownian motion
TL;DR: In this paper, a survey on the existence or absence of a riskless gain (arbitrage) in fractional Brownian motion based stock price models is presented, pointing out the importance of the chosen class of admissible trading strategies.
References
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Book
Singular Integrals and Differentiability Properties of Functions.
TL;DR: Stein's seminal work Real Analysis as mentioned in this paper is considered the most influential mathematics text in the last thirty-five years and has been widely used as a reference for many applications in the field of analysis.
Book
Continuous martingales and Brownian motion
Daniel Revuz,Marc Yor +1 more
TL;DR: In this article, the authors present a comprehensive survey of the literature on limit theorems in distribution in function spaces, including Girsanov's Theorem, Bessel Processes, and Ray-Knight Theorem.
Journal ArticleDOI
Linear Operators. Part I: General Theory.
TL;DR: Dunford and Schwartz as discussed by the authors provided a comprehensive survey of the general theory of linear operations, together with applications to the diverse fields of more classical analysis, and emphasized the significance of the relationships between the abstract theory and its applications.