Results 41 to 50 of about 92,103 (370)
Averaging principles for mixed fast-slow systems driven by fractional Brownian motion [PDF]
Kyoto Journal of Mathematics, 2020 We focus on fast-slow systems involving both fractional Brownian motion (fBm) and standard Brownian motion (Bm). The integral with respect to Bm is the standard Ito integral, and the integral with respect to fBm is the generalised Riemann-Stieltjes ...
B. Pei, Y. Inahama, Yong Xu
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Search efficiency of discrete fractional Brownian motion in a random distribution of targets
Physical Review Research, 2021 Efficiency of search for randomly distributed targets is a prominent problem in many branches of the sciences. For the stochastic process of Lévy walks, a specific range of optimal efficiencies was suggested under variation of search intrinsic and ...
S. Mohsen J. Khadem +2 more
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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
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Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions [PDF]
, 2012 We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter $H>1/2$). This maximum principle specifies a system of equations that the optimal
Han, Yuecai, Hu, Yaozhong, Song, Jian
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Operator Fractional Brownian Motion and Martingale Differences
Abstract and Applied Analysis, 2014 It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays an important role in both
Hongshuai Dai +2 more
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Averaging dynamics driven by fractional Brownian motion [PDF]
Annals of Probability, 2019 We consider slow / fast systems where the slow system is driven by fractional Brownian motion with Hurst parameter $H>{1\over 2}$. We show that unlike in the case $H={1\over 2}$, convergence to the averaged solution takes place in probability and the ...
Martin Hairer, Xue-Mei Li
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Path Properties of a Generalized Fractional Brownian Motion [PDF]
Journal of theoretical probability, 2020 The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power-law shape function and non-stationary ...
Tomoyuki Ichiba, G. Pang, M. Taqqu
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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.
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Linear filtering with fractional Brownian motion in the signal and observation processes [PDF]
, 1999 Integral equations for the mean-square estimate are obtained for the linear filtering problem, in which the noise generating the signal is a fractional Brownian motion with Hurst index h∈(3/4,1) and the noise in the observation process includes a ...
Anh, Vo Van +2 more
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Anticipated BSDEs Driven by Fractional Brownian Motion with a Time-Delayed Generator
Mathematics, 2023 This article describes a new form of an anticipated backward stochastic differential equation (BSDE) with a time-delayed generator driven by fractional Brownian motion, further known as fractional BSDE, with a Hurst parameter H∈(1/2,1).
Pei Zhang +2 more
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