טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentNeuman Eyal
SubjectSample Path Properties of Volterra Processes
DepartmentDepartment of Industrial Engineering and Management
Supervisor Professor Leonid Mytnik
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 .