Matrix-valued exponential martingale


Posted online: 2019-01-03 08:28:23Z by Andrea Pascucci75

Cite as: P-190103.1

  • Probability
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Problem's Description

Let $X$ be a matrix-valued Ito process $$dX_{t}=u_{t}dt+v_{t}dW_{t}$$ where $u$ and $v$ are $d\times d$-matrices, with $d\ge 2$, and $W$ is a real Brownian motion. Consider the exponential $$Q_{t}=\text{Exp}(X_{t}).$$ Under what conditions on $u,v$ is $Q$ a local martingale?

  1. Book Continuous martingales and Brownian motion

    pp. xiv+602, year of publication: 1999fulltext

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  • Created at: 2019-01-03 08:28:23Z