Sentence examples for exists a random variable from inspiring English sources
end{aligned} (3.19) Then from (3.18) and (3.19), we deduce that there exists a random variable (rho_{2} omega)) for all (mathbb{P} -a.e.
Suppose that: (({mathcal {H}}_{5})) : For every (x, y:Omegato X), random variables, there exists a random variable (z: Omegato X) such that, for every (omegainOmega), ((x omega ),z omega))), ((y omega),z omega))in X_{preceq}).
A BC is said to be stochastically degraded or degraded if there exists a random variable Y 1 ~ which has the same conditional pdf as Y1 given X, such that X → Y 1 ~ → Y 2 forms a Markov chain.
Since {Z n } is bounded within [ 0,1] and the supermartingale, from the martingale convergence theorem, there exists a random variable Z ∞ where the sequence {Z n } converges with probability 1 as n→∞.
From (({mathcal {H}}_{5})), there exists a random variable (z: Omegato X) such that, for every (omegainOmega), ((x omega),z omega))), ((x_{0} omega),z omega))in X_{preceq}).
By Taylor's formula, there exists a random variable (eta^{varepsilon}(t)) taking values in ((0,1)) such that bbigl(X^{varepsilon}_{t}bigr -bbigl(X^{0}_{t}bigr -bbiglgl(X^{0}_{t}+eta^{varepsilon}(t) bigr(X^{varepsilon}_{t}-X^{0}_{t}bigr)bigr) timesbigl(X^{varepsilon}_{t}-X^{0}_{t}bigr).
Therefore, we prove that there exist a random variable (rho_{3} omega)) and (T_{3B} omega)>0) such that for (mathbb{P} -a.e.
end{aligned} (3.17) Combining estimates (3.16) and (3.17), we prove that there exist a random variable (rho_{2} omega)) and (T_{2B} omega)>0) such that, for (mathbb{P} -a.e.
There exist a random variable (r_{1} omega)>0) and a bounded ball (B_{0}) of E centered at 0 with random radius (r_{0} omega)>0) such that for any bounded non-random set B of E, there exists a deterministic (T(B leq-1) such that the solution (psi(t,omega;psi(tau,omega))=(u(t,omega),B leq-1t,omega))^{T}) of (4.2) with initial value ((u_{0}, u_{1}+varepsuchn u_{0})^{that B) sathefiesolution-a.s.
These inequalities exist if a random variable ξ satisfies the condition defined as P | ξ | ≤ t ≤ αt (30) P | ξ | ≥ t ≤ e − βt (31).
For R there exists a random fixed point which is a random variable ξ : Ω → C such that ξ = R for any ω (cf. [5 7]).
