A Rate-optimal Trigonometric Series Expansion of the Fractional Brownian Motion

An optimal series expansion of the multiparameter fractional Brownian motion ∗

We derive a series expansion for the multiparameter fractional Brownian motion. The derived expansion is proven to be rate optimal .

Optimal Portfolio Series Formula under Dynamic Appreciation Rate Uncertainty

A closed-form series solution formula for the problem of optimal portfolio diversification under dynamic (possibly, long-term-memory) appreciation rate uncertainty, for an investor with HARA utility, is discovered. To that end a calculus of variations method, recently introduced by the author, was extended. The usefulness of the obtained result is examined by means of solving a few guiding exam...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

HAGEN GILSING AND TOMMI SOTTINEN Power series expansions for fractional Brownian Motions

Fractional Brownian Motions (FBM) are selfsimilar Gaussian processes with hölder-continuous paths, that can be represented as fractional integrals (H > 12) or derivatives (H < 1 2) of Brownian Motions (BM), allow an stochastic calculus, have long-range memory and are of interest in finance and network traffic. For the theory and for the numerical simulation of FBM series expansions are of inter...