טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentEyal Neuman
SubjectSample Path Properties of Volterra Processes
DepartmentDepartment of Industrial Engineering and Management
Supervisor Full Professor Mytnik Leonid
Full Thesis textFull thesis text - English Version


Abstract


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 .