Problem bank

Problem 196 of 333MediumStochastic CalculusP196

Is tW minus the area under W a martingale?

  1. Let WW be a standard Brownian motion and define Xt=tWt−∫0tWs dsX_t = tW_t - \int_0^t W_s\,ds. Is XtX_t a martingale? What is its distribution at time tt?