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337,963
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 longrange 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 ..."
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Cited by 121 (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 longrange 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 ItôClark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motio ..."
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Cited by 201 (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 ItôClark representation formula and the Girsanov theorem for the functionals of a fractional Brownian
ON THE MIXED FRACTIONAL BROWNIAN MOTION
"... The mixed fractional Brownian motion is used in mathematical finance, in the modelling of some arbitragefree and complete markets. In this paper, we present some stochastic properties and characteristics of this process, and we study the αdifferentiability of its sample paths. Copyright © 2006 Mou ..."
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The mixed fractional Brownian motion is used in mathematical finance, in the modelling of some arbitragefree and complete markets. In this paper, we present some stochastic properties and characteristics of this process, and we study the αdifferentiability of its sample paths. Copyright © 2006
The Multiparameter fractional Brownian motion, to appear
 in Proceedings of VK60 Math Everywhere Workshop
, 2006
"... setindexed processes Summary. We define and study the multiparameter fractional Brownian motion. This process is a generalization of both the classical fractional Brownian motion and the multiparameter Brownian motion, when the condition of independence is relaxed. Relations with the Lévy fractiona ..."
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Cited by 7 (3 self)
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setindexed processes Summary. We define and study the multiparameter fractional Brownian motion. This process is a generalization of both the classical fractional Brownian motion and the multiparameter Brownian motion, when the condition of independence is relaxed. Relations with the Lévy
Simulation of generalized fractional Brownian motion
"... Abstract: We consider simulation of ϕsubGaussian processes that are weakly selfsimilar with stationary increments in the sense that they have the covariance function R(t, s) = 1 2 t2H + s2H − t − s2H) for some H ∈ (0, 1). Here such processes are referred to as processes of generalized fraction ..."
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fractional Brownian motion, since the second order structure of the processes is that of the fractional Brownian motion. This study is a continuation of joint research performed together with Tommi Sottinen in [1]. The simulation is based on a series expansion of the fractional Brownian motion due
FRACTIONAL BROWNIAN MOTION IN A NUTSHELL
"... Abstract. This is an extended version of the lecture notes to a minicourse devoted to fractional Brownian motion and delivered to the participants of 7th Jagna International Workshop. 1. ..."
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Abstract. This is an extended version of the lecture notes to a minicourse devoted to fractional Brownian motion and delivered to the participants of 7th Jagna International Workshop. 1.
Deconvolution of fractional Brownian motion yz
"... We show that a fractional Brownian motion with index H 2 (0; 1) can be represented as an explicit transformation of a fractional Brownian motion with index H 2 (0; 1). In particular, when H = 1=2 we obtain a deconvolution formula (or autoregressive representation) for fractional Brownian motion. ..."
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Cited by 7 (0 self)
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We show that a fractional Brownian motion with index H 2 (0; 1) can be represented as an explicit transformation of a fractional Brownian motion with index H 2 (0; 1). In particular, when H = 1=2 we obtain a deconvolution formula (or autoregressive representation) for fractional Brownian motion
Finite Approximations to Fractional Brownian Motion
"... In [TWS], the authors prove a theorem that states that the superposition of strictly On/Off sources converges to a Fractional Brownian Motion as the number of sources increases to infinity if the distributions of the On times and the Off times satisfy certain assumptions. In this paper we simulate f ..."
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In [TWS], the authors prove a theorem that states that the superposition of strictly On/Off sources converges to a Fractional Brownian Motion as the number of sources increases to infinity if the distributions of the On times and the Off times satisfy certain assumptions. In this paper we simulate
Nonlinear Filtering with Fractional Brownian Motion
 Appl. Math. Optim
"... Abstract. Our objective is to study a nonlinear filtering problem for the observation process perturbed by a Fractional Brownian Motion (FBM) with Hurst index 1 2 < H < 1. A reproducing kernel Hilbert space for the FBM is considered and a “fractional ” Zakai equation for the unnormalized opti ..."
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Cited by 6 (3 self)
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Abstract. Our objective is to study a nonlinear filtering problem for the observation process perturbed by a Fractional Brownian Motion (FBM) with Hurst index 1 2 < H < 1. A reproducing kernel Hilbert space for the FBM is considered and a “fractional ” Zakai equation for the unnormalized
Results 1  10
of
337,963