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On stochastic calculus related to financial assets without semimartingales
A-martingale weak k-order Brownian motion no-semimartingale utility maximization insider no-arbitrage viability hedging
2011/3/23
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to ...
From constructive field theory to fractional stochastic calculus. (I) An introduction: rough path theory and perturbative heuristics
fractional Brownian motion stochastic integrals rough paths
2011/2/22
Let B = (B1(t), . . . ,Bd(t)) be a d-dimensional fractional Brownian motion with Hurst index ≤ 1/4, or more generally a Gaussian process whose paths have the same local regularity. Defining properly...
Foliated stochastic calculus: Harmonic measures
Foliation diffusion process stochastic calculus
2011/2/24
In this article we present an intrinsec construction of foliated Brownian motion via stochastic calculus adapted to foli-ation.
In this paper we investigate a quantum stochastic calculus
built of creation, annihilation and number of particles operators
which fulfill some deformed commutation relations.
Namely, we introduce ...
Large deviations and stochastic calculus for large random matrices
large deviations random matrices non-commutative measure integration.
2009/5/18
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory e...