Continuous Local Martingale

ProbabilityTheoryStochasticProcesses A Stochastic Process is a continuous local martingale if

1. is a continuous, Adapted Process
3. stopping times the stopped process is a martingale

Note that for the stopping time , will be u.i. when is a true martingale.

The following conditions are sufficient for a CLM to be a martingale

• Bounded:
• Bounded in L2 is a Martingale
• Domination by an L1 R.V. is a u.i. Martingale