Simulation of Weakly Self-Similar Stationary Increment $${text{Sub}}_{varphi } {left( Omega right)}$$-Processes: A Series Expansion Approach期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Simulation of Weakly Self-Similar Stationary Increment $${text{Sub}}_{varphi } {left( Omega right)}$$-Processes: A Series Expansion Approach

Authors:

Yuriy?Kozachenko,Tommi?Sottinen author-information" > author-information__contact u-icon-before" > mailto:tommi.sottinen@helsinki.fi" title=" tommi.sottinen@helsinki.fi" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Olga?Vasylyk

Affiliation:

1.Mechanics and Mathematics Faculty, Department of Probability Theory and Math. Statistics,Taras Shevchenko Kyiv National University,Kyiv,Ukraine;2.Department of Mathematics and Statistics,University of Helsinki,Helsinki,Finland

Abstract:

We consider simulation of ${text{Sub}}_{varphi } {left( Omega right)}$ -processes that are weakly selfsimilar with stationary increments in the sense that they have the covariance function

$R{left( {t,s} right)} = frac{1}{2}{left( {t^{{2H}} + s^{{2H}} - {left| {t - s} right|}^{{2H}} } right)}$

for some H ∈ (0, 1). This means that the second order structure of the processes is that of the fractional Brownian motion. Also, if $H >frac{1} {2}$ then the process is long-range dependent. The simulation is based on a series expansion of the fractional Brownian motion due to Dzhaparidze and van Zanten. We prove an estimate of the accuracy of the simulation in the space C([0, 1]) of continuous functions equipped with the usual sup-norm. The result holds also for the fractional Brownian motion which may be considered as a special case of a ${text{Sub}}_{{{x^{2} } mathord{left/ {vphantom {{x^{2} } 2}} right. kern-nulldelimiterspace} 2}} {left( Omega right)}$ -process. AMS 2000 Subject Classification 60G18, 60G15, 68U20, 33C10

Keywords:

fractional Brownian motion φ -sub-Gaussian processes long-range dependence self-similarity series expansions simulation

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