Satellite Communication Networks in modern days has higher frequencies above 10GHZ.Frequencies more than 10GHZ causes rain attenuation. In this paper, a channel model is defined to synthesize rain attenuation of 10GHZ and above. Previously, for satellite communication networks, Maseng-Bakken(M-B)model is used which is a time series synthesizer proposed based on Stochastic Differential equations...

Next to the shortest path distance, the second most popular distance function between vertices in a graph is the commute distance (resistance distance). For two vertices u and v, the hitting time Huv is the expected time it takes a random walk to travel from u to v. The commute time is its symmetrized version Cuv = Huv + Hvu. In our paper we study the behavior of hitting times and commute dista...

We build a family of Markov chains on a sphere using distance-based long-range connection probabilities to model the decentralized message-passing problem that has recently gained significant attention in the small-world literature. Starting at an arbitrary source point on the sphere, the expected message delivery time to an arbitrary target on the sphere is characterized by a particular expect...

We present some exact formulas for hitting probabilities and hitting numbers of one or several levels for a Lévy process {Xt | t ≥ 0} with no negative jumps, starting at zero. Let Nx be the number of visits of level x ∈ R and define τx = inf{t > 0 | Xt = x}. We determine the Laplace transform of f(x) = P[τx < ∞], x > 0. The counting variable Nx is finite if and only if EX1 6= 0 and the paths of...

Let {Yn}n∈Z+ be a sequence of random variables in R and let A ⊂ R. Then P{Yn ∈ A for some n} is the hitting probability of the set A by the sequence {Yn}. We consider the asymptotic behavior, as m → ∞, of P{Yn ∈ mA, some n} = P{hitting mA} whenever (1) the probability law of Yn/n satisfies the large deviation principle and (2) the central tendency of Yn/n is directed away from the given set A. ...

Let ”Yn•n∈Z+ be a sequence of random variables in R d and let A ⊂ Rd: Then P”Yn ∈ A for some n• is the hitting probability of the set A by the sequence ”Yn•. We consider the asymptotic behavior, as m → ∞, of P”Yn ∈ mA; some n• = P”hitting mA• whenever (1) the probability law of Yn/n satisfies the large deviation principle and (2) the central tendency of Yn/n is directed away from the given set ...

A set S that has a non-empty intersection with every set in a collection of sets C is called a hitting set of C. If no element can be removed from S without violating the hitting set property, S is considered to be minimal. Several interesting problems can be partly formulated as ones that a minimal hitting set or more ones have to be found. Many of these problems are required for proper soluti...

2 Hitting times 3 2.1 Typical hitting times are large . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Exponential mixing on spatial graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Expected hitting times degenerate to the stationary distribution . . . . . . . . . . . . . . . . 6 2.4 The case of one dimension . . . . . . . . . . . . . . . ....