Lecture 6: Functional limit theorems for financial markets with long-range dependence

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* General conditions of weak convergence

- Convergence of sums

- Multiplicative scheme

* Monotonicity along the diagonal of a triangular matrix in the Cholesky decomposition of a positive definite Toeplitz matrix

- Prediction of a stationary stochastic process

- Application to fractional Brownian motion

* High-frequency trading with fractional Brownian motion