Sentence examples for mutually singular as from inspiring English sources

We denote by (overline {mathcal {P}}_{W}) the set of all local martingale measures P for which (widehat {a}) is well-defined and takes values in (mathbb {S}^{>0}_{n} P -a.e.. Note that the measures in (overline {mathcal {P -a.e}) could be mutually singular, as noted in Soner et al. (2011).

Moreover, the singular part can be (uniquely again) decomposed in a sum of a purely atomic and a nonatomic measure (the Cantor part) (see [31], for instance): ν s = ν n s + ν p a. Thus the measure ν can be decomposed as a sum of three mutually singular measures: the Lebesgue part, the Cantor part and the singular (or jump) part, cf. [16, 32] ν = ν a c + ν n s + ν s.

We classify them and as a consequence we obtain that different parameters yield mutually singular Markov measure, extending the classical result of Kakutani.

This result provides an extension of the approach of Herdegen and Schweizer (2016) to the case of mutually singular priors.

There are many Markov chains on infinite dimensional spaces whose one-step transition kernels are mutually singular when starting from different initial conditions.

In this way our approach extends in a natural way the setting ofHerdegen and Schweizer (2016) to the case of mutually singular priors.

We study the concept of financial bubbles in a market model endowed with a set ({mathcal {P}}) of probability measures, typically mutually singular to each other.

Although "tefillin" is technically the plural form (the singular being "tefillah"), it is loosely used as a singular as well.

The meanings are as multiple and singular as its form.

The adequate moving object is the "proper entity" of a thing (Peter Auriol) or the singular as singular (Ockham).

However, the source of inequity may not be as singular as socio-economic position.