Fractional Brownian Motion and the Markov Property
Copyright policy )Fractional Brownian Motion and the Markov Property
Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This representation leads naturally to: - An efficient algorithm to approximate the process. - An infinite dimensional ergodic theorem which applies to functionals of the type $integral_0^t phi(V_h(s)) ds $ where $V_h(s)=integral_0^t h(t-u) dB_u$ and $B$ is a standard Brownian motion.
9 pages
60A10, Numerical Approximation, Functional limit theorems; invariance principles, 60FXX;60J25;60G15;65U05, Markov processes, Probability (math.PR), Gaussian processes, Probabilistic methods, stochastic differential equations, Markov Processes, Ergodic Theorem, 65U05, 60J25, 60G15, FOS: Mathematics, Continuous-time Markov processes on general state spaces, 26A33, 60FXX, numerical approximation, Mathematics - Probability, ergodic theorem
60A10, Numerical Approximation, Functional limit theorems; invariance principles, 60FXX;60J25;60G15;65U05, Markov processes, Probability (math.PR), Gaussian processes, Probabilistic methods, stochastic differential equations, Markov Processes, Ergodic Theorem, 65U05, 60J25, 60G15, FOS: Mathematics, Continuous-time Markov processes on general state spaces, 26A33, 60FXX, numerical approximation, Mathematics - Probability, ergodic theorem
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