## Abstract

We have shown that if one invests in the outcome of a random variable X, where investment consists of gambling at any odds, then every bit of description of X increases the doubling rate by one bit. However, if the provider of the information has access only to V, a random variable jointly distributed with X, then this maximal efficiency is not generally possible. We find the increase Δ(R) in doubling rate for a description of V at rate R for the jointly Gaussian and jointly binary cases. We investigate the extension to multivariate Gaussian random variables. We prove a general result for the derivative of Δ(R) at R = 0. We then consider the problem in which there are k separate encoders and each observers a random variable V_{i} correlated with X. We find how efficiently these encoders, without cooperation, help the investor who is interested in X.

Original language | English (US) |
---|---|

Number of pages | 1 |

State | Published - 1995 |

Event | Proceedings of the 1995 IEEE International Symposium on Information Theory - Whistler, BC, Can Duration: Sep 17 1995 → Sep 22 1995 |

### Other

Other | Proceedings of the 1995 IEEE International Symposium on Information Theory |
---|---|

City | Whistler, BC, Can |

Period | 9/17/95 → 9/22/95 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics