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Brownian motion
, 2003
"... Dynamics of quantum systems which are stochastically perturbed by lin-ear coupling to the reservoir can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation). In order to work it out one needs to de-ne the ..."
Abstract
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-ne the quantum Brownian motion. As far as only its boson version has been known until recently, in the present paper we present the denition which makes it possible to consider the fermion Brownian motion as well.
Brownian Motion Reflected On Brownian Motion
- Probab. Theory Related Fields
, 2002
"... Introduction. We will investigate some aspects of the local time, parabolic measure and excursion theory of Brownian motion reected on Brownian motion. Reected Brownian motion in a domain with a time-varying boundary has appeared in several articles (Bass and Burdzy [BB1], Cranston and Le Jan [CLJ], ..."
Abstract
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Cited by 11 (2 self)
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Introduction. We will investigate some aspects of the local time, parabolic measure and excursion theory of Brownian motion reected on Brownian motion. Reected Brownian motion in a domain with a time-varying boundary has appeared in several articles (Bass and Burdzy [BB1], Cranston and Le Jan [CLJ
Limiting behaviors of the Brownian motions on
, 901
"... brownian motions on hyperbolic spaces 1 ..."
FRACTIONAL BROWNIAN MOTION AND DYNAMIC
, 2007
"... Cakir, Rasit, Fractional Brownian motion and dynamic approach to ..."
Arbitrage with fractional Brownian motion
- Math. Finance
, 1997
"... Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow long-range dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing such an arbitr ..."
Abstract
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Cited by 122 (0 self)
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Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow long-range dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing
Stochastic Analysis of the Fractional Brownian Motion
- POTENTIAL ANALYSIS
, 1996
"... Since the fractional Brownian motion is not a semimartingale, the usual Itô calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula, the Itô-Clark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motio ..."
Abstract
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Cited by 199 (11 self)
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Since the fractional Brownian motion is not a semimartingale, the usual Itô calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula, the Itô-Clark representation formula and the Girsanov theorem for the functionals of a fractional Brownian
• Brownian motion
"... • Fluctuation-dissipation theoremBrownian particles small particles (10nm-5µm) dispersed in a solvent (diluted milk) The erratic motion of pollen suspended in water was observed and described by Robert Brown in 1827Coarse-grained picture The fluid described as a continuum medium obeying hydrodynamic ..."
Abstract
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• Fluctuation-dissipation theoremBrownian particles small particles (10nm-5µm) dispersed in a solvent (diluted milk) The erratic motion of pollen suspended in water was observed and described by Robert Brown in 1827Coarse-grained picture The fluid described as a continuum medium obeying
Results 1 - 10
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5,936
