• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.9-26
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• 2022

The purpose of this work is to study the existence and continuous dependence on neutral stochastic partial integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion with Hurst parameter $H{\in}({\frac{1}{2}},\;1)$. We use the theory of resolvent operators developed in Grimmer [19] to show the existence of mild solutions. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.923-935
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• 2023

In this paper, we will discuss existence of solution of square-mean pseudo almost automorphic solution for fractional stochastic evolution equations driven by G-Brownian motion which is given as ^c₀D^𝛼_𝜌 Ψ_𝜌 = 𝒜(𝜌)Ψ_𝜌d𝜌 + 𝚽(𝜌, Ψ_𝜌)d𝜌 + ϒ(𝜌, Ψ_𝜌)d ⟨ℵ⟩_𝜌 + χ(𝜌, Ψ_𝜌)dℵ_𝜌, 𝜌 ∈ R. Furthermore, we also prove that solution of the above equation is unique by using Lipschitz conditions and Cauchy-Schwartz inequality. Moreover, examples demonstrate the validity of the obtained main result and we obtain the solution for an equation, and proved that this solution is unique.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.179-184
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• 2005

Empirical findings on interet rate dynamics imply that short rates show some long memories and non-Markovin. It is well-known that fractional Brownian motion(fBm) is a proper candidate for modelling this empirical phenomena. fBm, however, is not a semimartingale process. For this reason, it is very hard to apply such processes for asset price modelling. With some modifications, this paper investigate the fBm interest rate theory, and obtain a pure discount bond price and Greeks.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.649-663
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• 2002

We consider an unlimited fluid queueing model which has Fractional Brownian motion(FBM) as an input and a single server of constant service rate. By using the result of Duffield and O'Connell(6), we investigate the asymptotic tail-distribution of the stationary work-load. When there are multiple homogeneous FBM inputs, the workload distribution is similar to that of the queue with one FBM input; whereas for the heterogeneous sources the asymptotic work-load distributions is dominated by the source with the largest Hurst parameter.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1501-1509
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• 2011

In this study, assume that the stock price obeys the stochastic differential equation driven by mixed fractional Brownian motion, and the short rate follows the Vasicek model. Then, the Black-Scholes partial differential equation is held by using fractional Ito formula. Finally, the pricing formulae of the barrier option are obtained by partial differential equation theory. The results of Black-Scholes model are generalized.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.411-420
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• 2013

We consider fractional Gussian noise and FARIMA sequence with Gaussian innovations and show that the suitably scaled distributions of the FARIMA sequences converge to fractional Gaussian noise in the sense of finite dimensional distributions. Finally, we figure out ACF function and estimate the self-similarity parameter H of FARIMA(0, $d$, 0) by using R/S method.

• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.481-492
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• 2017

This paper investigates a convergence rate of a test statistics given by two scale sampling method based on $A\ddot{i}t$-Sahalia and Jacod (Annals of Statistics, 37, 184-222, 2009). This statistics tests for longitudinal data having the existence of long memory dependence driven by fractional Brownian motion with Hurst parameter $H{\in}(1/2,\;1)$. We obtain an upper bound in the Kolmogorov distance for normal approximation of this test statistic. As a main tool for our works, the recent results in Nourdin and Peccati (Probability Theory and Related Fields, 145, 75-118, 2009; Annals of Probability, 37, 2231-2261, 2009) will be used. These results are obtained by employing techniques based on the combination between Malliavin calculus and Stein's method for normal approximation.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.295-304
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• 2015

This paper considers the problem of estimation of the Hurst parameter H ${\in}$ (1/2, 1) from longitudinal data with the error term of a fractional Brownian motion with Hurst parameter H that gives the amount of the long memory of its increment. We provide a new estimator of Hurst parameter H using a two scale sampling method based on $A{\ddot{i}}t$-Sahalia and Jacod (2009). Asymptotic behaviors (consistent and central limit theorem) of the proposed estimator will be investigated. For the proof of a central limit theorem, we use recent results on necessary and sufficient conditions for multi-dimensional vectors of multiple stochastic integrals to converges in distribution to multivariate normal distribution studied by Nourdin et al. (2010), Nualart and Ortiz-Latorre (2008), and Peccati and Tudor (2005).

• Mass Spectrometry Letters
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• v.6 no.4
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• pp.91-98
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• 2015

The Brownian motion or Wiener process, as the physical model of the stochastic procedure, is observed as an indexed collection random variables. Stochastic procedure are quite influential on the confinement potential fluctuation in the quadrupole ion trap (QIT). Such effect is investigated for a high fractional mass resolution Δm/m spectrometry. A stochastic procedure like the Wiener or Brownian processes are potentially used in quadrupole ion traps (QIT). Issue examined are the stability diagrams for noise coefficient, η=0.07;0.14;0.28 as well as ion trajectories in real time for noise coefficient, η=0.14. The simulated results have been obtained with a high precision for the resolution of trapped ions. Furthermore, in the lower mass range, the impulse voltage including the stochastic potential can be considered quite suitable for the quadrupole ion trap with a higher mass resolution.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.165-171
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• 2020

In this paper we consider a mixed fractional Brownian motion (mfBm) with jumps. The prices of European barrier options can be evaluated by solving a partial integro-differential equation (PIDE) with variable coefficients, which is derived from the mfBm with jumps. The 2-step backward differentiation formula (BDF2 method) proposed in [6] is applied with the second-order convergence rate in the time and spatial variables. Numerical simulations are carried out to observe the convergence behaviors of the BDF2 method under the mfBm with the Kou model.