M.Sc Student | Neuman Eyal |
---|---|

Subject | Sample Path Properties of Volterra Processes |

Department | Department of Industrial Engineering and Management |

Supervisor | PROF. Leonid Mytnik |

Full Thesis text |

We consider the regularity of sample paths of Volterra processes .

These processes are defined as stochastic integrals

*
M(t)=∫ _{0}^{t}
F(t,r)dX(r), t≥0*

where
X is a semimartingale
and F is a deterministic real-valued function. We derive the information
on the modulus of continuity for these processes under regularity assumptions
on the function F and show that
M(t) has ``worst'' regularity
properties at times of jumps of X(t). We apply our results to obtain
precise bounds on Hölder exponents of M(t) at different times t in
the case of the particular kernel *
F(t,r)=(t-r) ^{d}*. In this
case, we also study the spectrum of singularities of
M(t) if
X is
a Lévy process .