classical fractional Brownian motion
Stochastic delay evolution equations driven by sub fractional Brownian motion
... Remark . A remarkable fact is that the decay rate γ is independent of H. Indeed, in the case of considering a Q-Brownian motion, i.e., the case H = /, instead of our sub-fBm S H Q , the condition on λ ...
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Multifractal random walks with fractional Brownian motion via Malliavin calculus
... The data that we used in order to check the leverage effect and the long-range de- pendence come from S&P 500 index with a frequency of 15 seconds from 2012-02-28 to 2012-06-26, 131011 points. We compare the ...
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Extremes of a(t)-locally stationary Gaussian random fields
... The classical Central Limit Theorem and its ramifications show that the Gaussian model is a natural and correct paradigm for building an approximate solution to many otherwise unsolvable problems encountered in ...
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Stochastic modified Boussinesq approximate equation driven by fractional Brownian motion
... The fractional Brownian motion (FBM) is a family of Gaussian process which is indexed by the Hurst parameter H ∈ (, ...the classical Itô stochastic integral to FBM ...by fractional ...
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Evaluation of Geometric Asian Power Options under Fractional Brownian Motion
... In this paper, we first consider the geometric Asian options with constant risk-free rate and dividend rate under FBM, and derive the call-put parity. Furthermore, we discuss the geometric Asian power options. Finally, ...
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Ruin problems of a two-dimensional fractional Brownian motion risk process
... In classical risk theory, the surplus process of an insurance company is modeled by the compound Poisson or the general compound renewal risk process. For both applied and theoretical investigations, calculation ...
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Long range dependent processes and fractional Brownian motion
... on classical statistical results of statio n ary ...e classical approach were always studied under the assum ption th a t th e underlying random variables were independent, continue to hold under certain ...
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Arbitrage with fractional brownian motion?
... years fractional Brownian motion has been suggested to replace the classical Brownian motion as driving process in the mod- elling of many real world phenomena, including stock ...
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Cylindrical fractional Brownian motion in Banach spaces
... Fractional Brownian motion (fBm) has become very popular in recent years as driving noise in stochastic equations, in particular as an alternative to the classical Wiener ...
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A Wick functional limit theorem and applications to fractional Brownian motion
... Obviously, the standard reference on weak convergence is the monograph by Billingsley (1968). The characterization of weak convergence of discrete Wiener integrals to the contin- uous Wiener integrals in Theorem 1.4 is ...
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Nonlocal stochastic integro differential equations driven by fractional Brownian motion
... that fractional Brownian motion (fBm, for short) is a family of cen- tered Gaussian processes with continuous sample paths indexed by the Hurst parameter H ∈ (, ...
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On the non Lipschitz stochastic differential equations driven by fractional Brownian motion
... and they presented many meaningful results [–]. But, to the best of our knowledge, the existence and uniqueness of solutions of SDEs driven by fBm with a non-Lipschitz condition have not been considered. Since fBm is ...
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Controllability of a stochastic functional differential equation driven by a fractional Brownian motion
... study fractional order differential equations of Sobolev-type (see [14, 15] and the refer- ences ...Sobolev-type fractional nonlocal dynamical equations in Banach spaces is shown in ...the fractional ...
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Controllability of a Stochastic Neutral Functional Differential Equation Driven by a fBm
... • The functions G , f and σ are Borel functions with some suitable conditions. The paper is organized as follows. In Section 2, we represent some preliminaries for stochastic integral of fractional Brownian ...
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Transfer Principle for nth Order Fractional Brownian Motion with Applications to Prediction and Equivalence in Law
... order fractional Brownian motion by using the Mandelbrot–Van Ness representation ...order fractional Brownian motion B H (n) of Hurst index H ∈ (n − 1, n) by using the ...
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Boundary controllability of nonlocal Hilfer fractional stochastic differential systems with fractional Brownian motion and Poisson jumps
... the fractional stochastic differential equations with Hilfer fractional derivative, with Poisson jumps and optimal ...Hilfer fractional stochastic differential equations with fractional ...
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Malliavin calculus for backward stochastic differential equations and stochastic differential equations driven by fractional Brownian motion and numerical schemes
... by Brownian motion is essentially based on the method of time discretization and has a long ...by fractional Brownian motion, because the fraction Brownian motion B H is ...
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Modelling of Straitened Sedimentation Process in Bidisperse Suspension with Inter-Fractional Coagulation
... In the absence of the sedimentation ( u 2 ≅ 0 ) consolidation of aggregates occurs due to Brownian coagulation. Such a situation can occur in those cases where, for example, aggregate sizes are sufficiently small ...
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Fluctuation Analysis to Sequence of Ore-forming Element Based on Fractal-Jump Model
... In addition, due to the influence of material sources in the deep part of the earth, some unexpected events will occur, resulting in local aggregation or content anomalies in random sequences, that is called jumping ...
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An Ensemble Method of the Relationship between Diffusion Coefficient and Entropy in the Classical Brownian Motion
... has a decay time γ −1 , where α = M γ. In general, the mass of the particle is very small in mi- cro/nano scale. The inertial term can be ignored, compared with the viscosity term. That is in the low Reynolds number ...
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