Probability Commons^™

Shadow Casting Phenomena At Newgrange, Frank Prendergast

Articles

A digital model of the Newgrange passage tomb and surrounding ring of monoliths known as the Great Circle is used to investigate sunrise shadow casting phenomena at the monument. Diurnal variation in shadow directions and lengths are analysed for their potential use in the Bronze Age to indicate the passage of seasonal time. Computer-aided simulations are developed from a photogrammetric survey to accurately show how three of the largest monoliths, located closest to the tomb entrance and archaeologically coded GC1, GC-1 and GC-2, cast their shadows onto the vertical face of the entrance kerbstone, coded K1. The phenomena occur at …

Characterization Of Matrix Variate Normal Distributions, A.K. Gupta, T. Varga

Mathematical Sciences Technical Reports (MSTR)

In this paper, it is shown that two random matrices have a joint matrix variate distribution if conditioning each one on the other the resulting distributions satisfy certain conditions. A general result involving more than two matrices is also proved.

Characterization Of Joint Density By Conditional Densities, A.K. Gupta, T. Varga

Mathematical Sciences Technical Reports (MSTR)

In this paper the relationship between joint density and conditional densities is studied. An explicit formula is given for obtaining the joint density from the conditional ones. It is illustrated for the case of bivariate normal distribution.

On The Optimal Reward Function Of The Continuous Time Multiarmed Bandit Problem, José Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

The optimal reward function associated with the so-called "multiarmed bandit problem" for general Markov-Feller processes is considered. It is shown that this optimal reward function has a simple expression (product form) in terms of individual stopping problems, without any smoothness properties of the optimal reward function neither for the global problem nor for the individual stopping problems. Some results relative to a related problem with switching cost are obtained.

A Model Of Dc Glow Discharges With Abnormal Cathode Fall, Karl H. Schoenbach, Hao Chen, G. Schaefer

Bioelectrics Publications

A model for an abnormal glow discharge, including a self‐consistent analysis of the cathode fall, was developed. It combines microscopic particle simulation by means of Monte Carlo methods with a fluid model of the gas discharge. The model allows calculations of the steady‐state electrical field distribution, the charged‐particle densities, and the current densities along the axis of the discharge. The model was used to simulate a glow discharge in 80% He and 20% SF₆ at a pressure of 8 Torr with a current density of 1 A/cm². The computed discharge voltage agrees well with measured values. The …

Some Estimates For Finite Difference Approximations, José-Luis Menaldi

Mathematics Faculty Research Publications

Some estimates for the approximation of optimal stochastic control problems by discrete time problems are obtained. In particular an estimate for the solutions of the continuous time versus the discrete time Hamilton-Jacobi-Bellman equations is given. The technique used is more analytic than probabilistic.

On Asymptotic Behavior Of Stopping Time Problems, Jose Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

No abstract provided.

Large Deviation Local Limit Theorems For Ratio Statistics, Sanjeev V. Sabnis

Mathematics & Statistics Theses & Dissertations

Let {T„, n > 1} be an arbitrary sequence of non-lattice random variables and {S_n, n > 1} be another sequence of positive non-lattice random variables. Let the two sequences be independent. Let Ø_1n and Ø_2n be the moment genereating functions of {Tn, n > 1} and { S_n,n > 1} respectively. Let {a_n} be a sequence of real numbers such that a_n —»• oo.

Limit Theorems In The Area Of Large Deviations For Some Dependent Random Variables, Narasinga Rao Chaganty, Jayaram Sethuraman

Mathematics & Statistics Faculty Publications

A magnetic body can be considered to consist of n sites, where n is large. The magnetic spins at these n sites, whose sum is the total magnetization present in the body, can be modelled by a triangular array of random variables (X(n) 1,..., X(n) n). Standard theory of physics would dictate that the joint distribution of the spins can be modelled by dQ_n(x) = z_n^-1 exp[ -H_n(x)]Π dP(x_j), where x = (x₁,..., x_n) ∈ Rⁿ, where H_n is the Hamiltonian, z_n is …

Reflected Diffusion Processes With Jumps, José-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

A stochastic differential equation of Wiener-Poisson type is considered in a d-dimensional bounded region. By using a penalization argument on the domain, we are able to prove the existence and uniqueness of solutions in the strong sense. The main assumptions are Lipschitzian coefficients, either convex or smooth domains and a regular outward reflecting direction. As a direct consequence, it is verified that the reflected diffusion process with jumps depends on the initial date in a Lipschitz fashion.

Conformational Analysis Of Nonsteroidal Estrogen Analogs, Robert N. Spady

Loma Linda University Electronic Theses, Dissertations & Projects

In target tissue, estrogens initiate a series of events, ending in protein synthesis, by binding to a cytoplasmic receptor. Once the estrogen binds, the receptor complex is activated--a process including dimerization of the estrogen complex with another subunit. In order to study the possible receptor-ligand interactions, conformational analysis was performed on several nonsteroidal estrogen analogs, using the CAMSEQ8 molecular mechanics program.

The probability that a molecule will exist in a given conformational energy well depends both on the energy and the shape of the well. A method has been previously worked out to calculate probabilities using both of these variables, …

On The First Passage Time Distribution For A Class Of Markov Chains, Mark Brown, Narasinga Rao Chaganty

Mathematics & Statistics Faculty Publications

Consider a stochastically monotone chain with monotone paths on a partially ordered countable set S. Let C be an increasing subset of S with finite complement. Then the first passage-time from i ∈ S to C is shown to be IFRA (increasing failure rate on the,av;rage). Several applications are presented including coherent systems, shock models, and convolutions of IFRA distributions.

Probability Driven Heuristic Nets, Lynn Robert Carter

Dissertations and Theses

Let a probability driven switch be defined as a switch of three input paths and three output paths. The status of the input paths defines a probability for each output path (as to whether it will generate a signal or not.) One output path is linked to one input path, so the results of the switch at time t can affect the switch at time t+1. A switch so constructed can be defined (by the probabilities) to take on the function of the standard logic gates (AND, OR, …) A net constructed of these switches can be “taught” by …