|M.Sc Student||Neuman Eyal|
|Subject||Sample Path Properties of Volterra Processes|
|Department||Department of Industrial Engineering and Management||Supervisor||Professor Leonid Mytnik|
|Full Thesis text|
We consider the regularity of sample paths of Volterra processes .
These processes are defined as stochastic integrals
M(t)=∫0t 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 .