Martingale Problem and Quadratic Family

Key Points

• Necessary conditions for the Girsanov transformation are derived from the martingale problem aspect of Markov processes.
• The uniqueness of the martingale problem is assumed within a quadratic family of generators, showing key insights.
• Generators for stationary reference Markov processes are examined, focusing on their positive values across all states.
• Predictable processes $a_t(i)$ and $b_t(i)$ play a crucial role in defining the quadratic family for Markov generators.