The Symbol of a Markov Semimartingale

We prove that every (nice) Feller process is an It^o process in the sense of Cinlar, Jacod, Protter and Sharpe (1980). Next we generalize the notion of the symbol and define it for this larger class of processes. As examples the solutions of stochastic differential equations are considered. The symbol is then used to derive a quick approach to the semimartingale characteristics as well as the generator of the process under consideration. Finally we give some examples of how our methods work for processes used in mathematical finance.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Technische Universität Dresden

Year

2009

Author dc:creator

• Schnurr, Alexander

Contributors dc:contributor

• Schilling, René L.
• Nollau, Volker
• Jacob, Niels

• Markov process
• semimartingale
• Itô process
• Feller semigroup
• generator
• symbol
• pseudo differential operator
• stochastic differential equation
• COGARCH process
• Markov Prozess
• Semimartingal
• Itô Prozess
• Feller Halbgruppe
• Erzeuger
• Pseudo-Differential-Operator
• stochastische Differentialgleichung
• COGARCH Prozess