Conditioned Martingales

Details Conditioned Martingales Conditioned Martingales

2012-03-12

arxiv.org/abs/1203.2587v1

Mathematics

Probability

Scientific paper

It is well-known that upward conditioned Brownian motion is a three-dimensional Bessel process, and that a downward conditioned Bessel process is a Brownian motion. We give an extremely simple proof for this result, which generalizes to any continuous local martingale and clarifies the role of finite vs infinite time in this setting. As a consequence, we can describe the law of regular diffusions that are conditioned upward or downward.

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