Motivated by optimal trade execution, this paper studies the temporal evolution of the shape of a limit order book over a time horizon that is large compared with the length of time between order book events, with the aim of approximating the transient distribution of the shape. Relying on the...

We consider a buffered queueing system that is fed by a Gaussian source and drained at a constant rate. The fluid offered to the system in a time interval (0,t] is given by a separable continuous Gaussian process Y with stationary increments. The variance function of Y is assumed to be regularly...

Consider a centered separable Gaussian process Y with a variance function that is regularly varying at infinity with index 2H[set membership, variant](0,2). Let [phi] be a 'drift' function that is strictly increasing, regularly varying at infinity with index [beta]H, and vanishing at the origin....