Basic concepts and techniques in the theory of stochastic processes introduction to Markov processes

2008 ◽  
pp. 2-18
Author(s):  
R. Vasudevan
Keyword(s):  
Stochastic Processes ◽  
Markov Processes ◽  
Basic Concepts

scholarly journals A stability result for linear Markovian stochastic optimization problems

2020 ◽  
Author(s):  
Adriana Kiszka ◽  
David Wozabal
Keyword(s):  
Stochastic Optimization ◽  
Stochastic Processes ◽  
Objective Function ◽  
Markov Processes ◽  
Optimization Problems ◽  
Stability Result ◽  
Extant Literature ◽  
Numerical Example ◽  
Optimal Values ◽  
Objective Value

Abstract In this paper, we propose a semi-metric for Markov processes that allows to bound optimal values of linear Markovian stochastic optimization problems. Similar to existing notions of distance for general stochastic processes, our distance is based on transportation metrics. As opposed to the extant literature, the proposed distance is problem specific, i.e., dependent on the data of the problem whose objective value we want to bound. As a result, we are able to consider problems with randomness in the constraints as well as in the objective function and therefore relax an assumption in the extant literature. We derive several properties of the proposed semi-metric and demonstrate its use in a stylized numerical example.

Markov processes for modeling and analyzing a new genetic mapping method

1993 ◽  
Vol 30 (04) ◽  
pp. 766-779 ◽  
Author(s):  
Eleanor Feingold
Keyword(s):  
Markov Chains ◽  
Genetic Mapping ◽  
Stochastic Processes ◽  
Markov Processes ◽  
Mapping Method ◽  
Central Issue ◽  
Boundary Crossing ◽  
Crossing Probabilities

This paper describes a set of stochastic processes that is useful for modeling and analyzing a new genetic mapping method. Some of the processes are Markov chains, and some are best described as functions of Markov chains. The central issue is boundary-crossing probabilities, which correspond to p-values for the existence of genes for particular traits. The methods elaborated by Aldous (1989) provide very accurate approximate p-values, as spot-checked against simulations.

scholarly journals The relationship between intensity and stochastic matrices for continuous-time discrete value stochastic non-homogeneous processes with Markov property

2017 ◽  
Vol 13 (3) ◽  
pp. 7244-7256
Author(s):  
Mi los lawa Sokol
Keyword(s):  
Markov Process ◽  
Stochastic Processes ◽  
Markov Processes ◽  
Continuous Time ◽  
Markov Property ◽  
Time Dependent ◽  
Stochastic Matrices ◽  
Homogeneous Markov Process ◽  
The Relationship ◽  
Time Form

The matrices of non-homogeneous Markov processes consist of time-dependent functions whose values at time form typical intensity matrices. For solvingsome problems they must be changed into stochastic matrices. A stochas-tic matrix for non-homogeneous Markov process consists of time-dependent functions, whose values are probabilities and it depend on assumed time pe- riod. In this paper formulas for these functions are derived. Although the formula is not simple, it allows proving some theorems for Markov stochastic processes, well known for homogeneous processes, but for non-homogeneous ones the proofs of them turned out shorter.

scholarly journals Generalised liouville processes and their properties

2020 ◽  
Vol 57 (4) ◽  
pp. 1088-1110
Author(s):  
Edward Hoyle ◽  
Levent Ali Menguturk
Keyword(s):  
Stochastic Processes ◽  
Markov Processes ◽  
Finite Time ◽  
Time Horizon ◽  
New Family ◽  
Terminal Values ◽  
Finite Time Horizon ◽  
Time Changes

AbstractWe define a new family of multivariate stochastic processes over a finite time horizon that we call generalised Liouville processes (GLPs). GLPs are Markov processes constructed by splitting Lévy random bridges into non-overlapping subprocesses via time changes. We show that the terminal values and the increments of GLPs have generalised multivariate Liouville distributions, justifying their name. We provide various other properties of GLPs and some examples.

Markov processes for modeling and analyzing a new genetic mapping method

1993 ◽  
Vol 30 (4) ◽  
pp. 766-779 ◽  
Author(s):  
Eleanor Feingold
Keyword(s):  
Markov Chains ◽  
Genetic Mapping ◽  
Stochastic Processes ◽  
Markov Processes ◽  
Mapping Method ◽  
Central Issue ◽  
Boundary Crossing ◽  
Crossing Probabilities

This paper describes a set of stochastic processes that is useful for modeling and analyzing a new genetic mapping method. Some of the processes are Markov chains, and some are best described as functions of Markov chains. The central issue is boundary-crossing probabilities, which correspond to p-values for the existence of genes for particular traits. The methods elaborated by Aldous (1989) provide very accurate approximate p-values, as spot-checked against simulations.

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