Results 11 to 20 of about 7,656 (241)
Arbitrage with Fractional Brownian Motion [PDF]
Mathematical 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 arbitrage.
L C G Rogers
exaly +3 more sources
The fractional mixed fractional brownian motion and fractional brownian sheet [PDF]
ESAIM: Probability and Statistics, 2007 Summary: We introduce the fractional mixed fractional Brownian motion and fractional Brownian sheet, and investigate the small ball behavior of its sup-norm statistic. Then, we state general conditions and characterize the sufficiency part of the lower classes of some statistics of the above process by an integral test.
El-Nouty, Charles, Charles El-Nouty
openaire +3 more sources
Fractional Brownian motion [PDF]
, 2013 Fractional Brownian motion is a nontrivial generalization of standard Brownian motion (Wie- ner process). Definition leaves independence of increments, whereas dependence is controlled by the Hurst index.
Rubín, Tomáš
openaire +3 more sources
Stochastic integration for tempered fractional Brownian motion [PDF]
Stochastic Processes and Their Applications, 2014 Mark M Meerschaert, Farzad Sabzikar
exaly +2 more sources
Fractional Brownian Motion [PDF]
, 2019 There are natural phenomena in which wide variability is commonly observed, most notably the weather. Any expectations of regularity, or independence of this year’s weather from the past or the future, are not borne out by tradition or folklore. Mandelbrot and Wallis [16.1] saw the essence of traditional knowledge expressed in the Old Testament ...
Oksana Banna +3 more
+6 more sources
Fractional Brownian Motions [PDF]
Acta Physica Polonica B, 2020 Properties of different models of fractional Brownian motions are discussed in detail. We shall collect here several possible ways of introducing and defining various possible fBms, discuss their properties, find how they are similar, and how they differ.
openaire +2 more sources
Asymptotics of the Persistence Exponent of Integrated Fractional Brownian Motion and Fractionally Integrated Brownian Motion [PDF]
Theory of Probability & Its Applications, 2022 Рассматривается вероятность персистентности для интегрированного дробного броуновского движения и дробно интегрированного броуновского движения с параметром $H$. Для интегрированного дробного броуновского движения обсуждается гипотеза Молчана- Хохлова и устанавливается асимптотическое поведение показателя персистентности при $H\to0$ и при $H\to1 ...
Aurzada, F., Kilian, M.
openaire +2 more sources
Oscillatory Fractional Brownian Motion [PDF]
Acta Applicandae Mathematicae, 2013 The authors ``introduce oscillatory analogues of fractional Brownian motion [(fBm)], subfractional Brownian motion [(sfBm)] and other related long range dependent Gaussian processes.'' According to them, the oscillatory fractional Brownian motion (ofBm) is a centered Gaussian process \(\xi ^{H}\), with parameter \(H\in (1/2,1)\) and covariance function
Bojdecki, T. +2 more
openaire +2 more sources
On Squared Fractional Brownian Motions [PDF]
, 2004 We have proved recently that fractional Brownian motions with Hurst parameter H in (0, 1/2) satisfy a remarkable property: their squares are infinitely divisible. In the Brownian motion case (the case H = 1/2), this property is completely understood thanks to stochastic calculus arguments.
Eisenbaum, N., Tudor, C.A.
openaire +2 more sources
Prediction law of fractional Brownian motion [PDF]
Statistics & Probability Letters, 2017 We calculate the regular conditional future law of the fractional Brownian motion with index $H\in(0,1)$ conditioned on its past. We show that the conditional law is continuous with respect to the conditioning path. We investigate the path properties of the conditional process and the asymptotic behavior of the conditional covariance.
Viitasaari, Lauri, Sottinen, Tommi
openaire +7 more sources