Sentence examples for be a sample path from inspiring English sources

A stochastic process is said to be a sample path solution to(3.76) with the initial condition if for any sample value of then satisfies (3.79).

For the Schrödinger operator on L2(R2) with the magnetic field which is a sample path of a stationary Gaussian random field, a Wegner type estimate applicable for the proof of the Anderson localization is proven by referring a recent method by Erdős and Hasler, and the theory of the Malliavin calculus.

which imply that satisfies (3.76), that is, is a sample path solution of (3.76).

If is a sample path solution of (3.76), then it is easy to check that is a solution of (3.81).

The works [2 4] are based on the idea of a random walk tour, which is a sample path of a random walk starting and ending at a fixed node.

For any values t k of the random variables τ k, the solution x ( t ; T 0, x 0, { t k } ) of the initial value problem for the impulsive equation with fixed points of impulses (1) will be called a sample path solution of RIDE (2).

The mapping (X_{t}( cdot,omega ): t in T to X_{t} omega ) in E) is called a sample path of the process corresponding to ω. Carrying out similar arguments as those of Lemma 15 in [25], we have the following lemma.

The key idea is to construct a sample path rooted at v, which has a higher probability than the optimal sample path rooted at u.

The key idea is to construct a sample path originated from node v based on the optimal sample path originated from node u and show that it occurs with a higher probability.

Let be any sample path solution of (3.76); then Lemma 3.39 implies (3.87).

Let us consider two identical copies of a sample path; that is, arrivals and fading for each of the users are the same in every slot.