A one-dimensional Brownian motion {B(t), 0 ≤ t}is a continuous-time, Markovian, real-valued stochastic process having continuous sample paths; its distribution is Gaussian with mean function E[B(t)] = μt and covariance function Cov[B(s), B(t)] = σ2 min (s, t). An n-dimensional Brownian motion is a stochastic process on n whose n components are independent one-dimensional Brownian motions. Markov processes.
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© 2001 Kluwer Academic Publishers
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Gass, S.I., Harris, C.M. (2001). BROWNIAN MOTION . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_89
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DOI: https://doi.org/10.1007/1-4020-0611-X_89
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