Extreme-value statistics of fractional Brownian motion bridges.

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

Parameter estimation for α-fractional bridges

Let α, T > 0. We study the asymptotic properties of a least squares estimator for the parameter α of a fractional bridge defined as dXt = −α Xt T−t dt + dBt, 0 6 t < T , where B is a fractional Brownian motion of Hurst parameter H > 12 . Depending on the value of α, we prove that we may have strong consistency or not as t → T . When we have consistency, we obtain the rate of this convergence as...

Large Modelling of Extremal Events

Modelling of Extremal Events (published by Springer) by Embrechts, Kluppelberg and Mikosch is truly a godsend. Coverage of the major topics related to extreme value theory is done in such a way that I was inspired to implement many of their various modeling techniques. The topics they cover include Brownian motion, domains of attraction, the generalized extreme value distribution, order statist...

Maximum Distributions of Noncolliding Bessel Bridges

The one-dimensional Brownian motion starting from the origin at time t = 0, conditioned to return to the origin at time t = 1 and to stay positive during time interval 0 < t < 1, is called the Bessel bridge with duration 1. We consider theN -particle system of such Bessel bridges conditioned never to collide with each other in 0 < t < 1, which is the continuum limit of the vicious walk model in...