Probability measure: Difference between revisions

==Example applications==
''MarketMarketNIGGRRProbability measures'' which assign probabilities to [[financial market]] spaces based on actual market movements are examplesalso of probability measures which are of interestused in [[mathematical finance]], e.g. in the pricing of [[financial derivativebiology]]s.<ref>''QuantitativeMathematical methodsMethods in derivatives pricingBiology'' by DomingoJ. TavellaDavid 2002Logan, William R. Wolesensky 2009 ISBN 0-471470-3944752587-58 [ page 11195]</ref> For instance, ain comparative [[risk-neutralsequence measureanalysis]] is a probability measure whichmay assumesbe thatdefined the current value of assets isfor the [[expectedlikelihood value]]that ofa thevariant futuremay payoffbe [[discounted]]permissible atfor thean [[risk-freeamino rateacid]]. If there is a unique probability measure that must be used to price assets in a market, then the market is called a [[complete market]]sequence.<ref>''IrreversibleDiscovering decisionsbiomolecular undermechanisms uncertaintywith computational biology'' by SvetlanaFrank I.Eisenhaber Boyarchenko, Serge Levendorskiĭ 20072006 ISBN 30-540387-7374534527-62 [ page 11127]</ref>
Not all measures that intuitively represent chance or likelihood are probability measures. For instance, although the fundamental concept of a system in [[statistical mechanics]] is a measure space, such measures are not always probability measures.<ref name=stern/> In general, in statistical physics, if we consider sentences of the form "the probability of a system S assuming state A is p" the geometry of the system does not always lead to the definition of a probability measure [[congruence relation|under congruence]], although it may do so in the case of systems with just one degree of freedom.<ref name=gut/>
Probability measures are also used in [[mathematical biology]].<ref>''Mathematical Methods in Biology'' by J. David Logan, William R. Wolesensky 2009 ISBN 0-470-52587-8 [ page 195]</ref> For instance, in comparative [[sequence analysis]] a probability measure may be defined for the likelihood that a variant may be permissible for an [[amino acid]] in a sequence.<ref>''Discovering biomolecular mechanisms with computational biology'' by Frank Eisenhaber 2006 ISBN 0-387-34527-2 [ page 127]</ref>
==See also==
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