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The transmission of scientific data over long distances is required to enable interplanetary science expeditions. Current approaches include transmitting all collected data or transmitting low resolution data to enable ground controller review and selection of data for transmission. Model-based data transmission (MBDT) seeks to increase the amount of knowledge conveyed per unit of data transmitted by comparing high-resolution data collected in situ to a pre-existing (or potentially co-transmitted) model. This paper describes the application of MBDT to gravitational data and characterizes its utility and performance. This is performed by applying the MBDT technique to a selection of gravitational data previously collected for the Earth and comparing the transmission requirements to the level required for raw data transmis-sion and non-application-aware compression. Levels of transmission reduction up to 31.8% (without the use maximum-error-thresholding) and up to 97.17% (with the use of maximum-error-thresholding) resulted. These levels significantly exceed what is possible with non-application-aware compression.
We study the information structure implied
by models in which the asset price is always risky and there are no arbitrage
opportunities. Using the martingale representation of Harrison and Kreps , a
claim takes its value from the stream of discounted expected payments. Equivalently,
a pricing-kernel is sufficient to value the payment stream. If a price process
is always risky, then either the payment or the discount factor must also be
continually risky. This observation substantially complicates the valuation of
contingent claims. Many classical option pricing formulas abstract from both
risky dividends and risky discount rates. In order to value contingent claims,
one of the assumptions must be abandoned.