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Boundary Crossing Probabilities of Jump Diffusion Processes to Time-Dependent Boundaries
The finite Markov chain imbedding technique has been used to compute the boundary crossing probabilities of one and higher-dimensional Brownian...
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Phase Transition in Inhomogenous Erdős-Rényi Random Graphs via Tree Counting
Consider the complete graph K n on n vertices where each edge e is independently open with probability p n ( e ) or closed otherwise. The edge...
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The Quality of Life Via Semi Markov Reward Modelling
The quality of life is recognized as an important element which is generally treated at least as primary or secondary criterion in most clinical...
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Reward Algorithms for Semi-Markov Processes
New algorithms for computing power moments of hitting times and accumulated rewards of hitting type for semi-Markov processes are developed. The...
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Controlling Bivariate Categorical Processes using Scan Rules
In this paper, we introduce a methodology for efficiently monitoring a health process that classify the intervention outcome, in two dependent...
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Decomposing Hitting Times of Walks on Graphs into Simpler Ones
Using the electric approach, we derive a formula that expresses an expected hitting time of a random walk between two vertices a and b of a graph G ...
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Approximating the distributions of runs and patterns
The distribution theory of runs and patterns has been successfully used in a variety of applications including, for example, nonparametric hypothesis...
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On the Accuracy of the MAP Inference in HMMs
In a hidden Markov model, the underlying Markov chain is usually unobserved. Often, the state path with maximum posterior probability (Viterbi path)...
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Exact distributions of constrained (k, ℓ) strings of failures between subsequent successes
Consider a sequence of binary (success–failure) random variables (RVs) ordered on a line. The number of strings with a constrained number of...
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Generating Functions of Waiting Times and Numbers of Visits for Random Walks on Graphs
In this paper, we consider some cover time problems for random walks on graphs in a wide class of waiting time problems. By using generating...
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1-Dependent Stationary Sequences for Some Given Joint Distributions of Two Consecutive Random Variables
We provide a method to construct a 1-dependent stationary sequence provided some mixing condition on the joint distribution of two consecutive random...
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The asymmetric n-player gambler’s ruin problem with ties allowed and simulation
The gambler’s ruin problems with more than two players for the symmetric and asymmetric cases have already been studied in the literature. Therefore,...
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A New Method of Approximating the Probability of Matching Common Words in Multiple Random Sequences
In this paper we consider R independent sequences of length T formed by independent, not necessarily uniformly distributed letters drawn from a...
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Ruin Analysis of a Threshold Strategy in a Discrete-Time Sparre Andersen Model
In this paper, we extend the methodology of Alfa and Drekic (ASTIN Bull 37:293–317,
2007 ) to analyze a discrete-time, delayed Sparre Andersen... -
The Sequential Occupancy Problem through Group Throwing of Indistinguishable Balls
The occupancy problem is generalized to the case where instead of throwing one ball at a time, a fixed size group of indistinguishable balls are...
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Runs of Markov Chains and Streaks in Baseball
We find the almost sure limits of the proportions of the total number of runs, and of the number of runs of a given length, over the number of...
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Uniform Accuracy of the Maximum Likelihood Estimates for Probabilistic Models of Biological Sequences
Probabilistic models for biological sequences (DNA and proteins) have many useful applications in bioinformatics. Normally, the values of parameters...
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On Success Runs of Length Exceeded a Threshold
Consider a sequence of n two state (success-failure) trials with outcomes arranged on a line or on a circle. The elements of the sequence are...
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Tail and dependence behavior of levels that persist for a fixed period of time
This work emerges from a study of the extremal behavior of a daily maximum sea water levels series, { X i } , presented in Draisma (Duration of...
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On the Normal Approximation for the Distribution of the Number of Simple or Compound Patterns in a Random Sequence of Multi-state Trials
Distributions of numbers of runs and patterns in a sequence of multi-state trials have been successfully used in various areas of statistics and...