Sentence examples for exists a continuous version from inspiring English sources

(2.7) Moreover, if inequality (2.3) is satisfied, then there exists a continuous version of the process (W_{S}^{varphi}), (tgeq0).

Then there exists a continuous version (tilde{X}(t)) of (X t)) which has the property that for every (varthetain 0,varsigma/eta)), there is a positive random variable (psi omega)) such that mathbb{P}biggl{ omega:sup_{0< vert t-s vert < psi omega), 0leq s,t< infty}frac{ vert tilde{X} t,omega -X t,omega -X trt }{ vert t-s vert ^{vartheta}}leq frac{2}{1-2^{-vartheta}}biggr} =1.

Then there exists a continuous version (tilde{X}(t)) of (X t)) which has the property that for every (varthetain 0,beta/alpha)), there is a positive random variable (varphi omega)) such that mathbf{P} biggl{ omega:sup_{0< |t-s|< varphi omega), 0leq s,t< +infty}frac{|tilde{X} t,omega -X t,omega -X tt-s|^{vartheta }}leq frac{2}{1-2^{-vartheta}} biggr} =1.

(i)  There exists a continuous function  :  such that (2.19).

(Hkl Suppose there exists a continuous function     such that.

There exists a continuous function (d(t geq0) for a.e.

There exists a continuous impulse mapping (I: I(M =N).

For, is completely continuous and there exists a continuous nondecreasing function such that for each, (2.18).

A continuous version is given below.

A continuous version of this inequality is presented in [15].

This process is null on the axes and has a continuous version.