Stochastic Processes, Markov Chains and Master Equations

2018 ◽  
pp. 269-289
Author(s):  
Wokyung Sung
Keyword(s):  
Markov Chains ◽  
Stochastic Processes ◽  
Master Equations

scholarly journals Lie Algebra Solution of Population Models Based on Time-Inhomogeneous Markov Chains

2012 ◽  
Vol 49 (02) ◽  
pp. 472-481 ◽  
Author(s):  
Thomas House
Keyword(s):  
Markov Chains ◽  
Stochastic Processes ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Natural Populations ◽  
Algebraic Method ◽  
Population Models ◽  
Physical Sciences ◽  
Solution Form ◽  
Social Applications

Many natural populations are well modelled through time-inhomogeneous stochastic processes. Such processes have been analysed in the physical sciences using a method based on Lie algebras, but this methodology is not widely used for models with ecological, medical, and social applications. In this paper we present the Lie algebraic method, and apply it to three biologically well-motivated examples. The result of this is a solution form that is often highly computationally advantageous.

scholarly journals Markov chains and the determination of fair premiums

1967 ◽  
Vol 4 (3) ◽  
pp. 265-268 ◽  
Author(s):  
Stefan Vajda
Keyword(s):  
Stochastic Process ◽  
Markov Chains ◽  
Stochastic Processes ◽  
Mathematical Theory ◽  
The Other ◽  
Main Stream ◽  
Other Hand ◽  
Pure Mathematics ◽  
The University

The relationships between actuarial and pure mathematics are curious. Actuaries have contributed to the development of mathematical theory: it is sufficient to mention, as examples, Fredholm of an earlier, and Cramér of a more recent generation. Scandinavian mathematicians, in particular, have been concerned with a very special type of stochastic process, reflected in the collective theory of risk, and the work of Philipson, Ammeter and others in this field is well known to readers of this Bulletin. However, the main stream of the theory of stochastic processes has little contact with actuarial applications.On the other hand, many actuaries have studied and assimilated pure mathematics and have thrown light on actuarial matters by describing their own preoccupations in the terminology of modern, often abstract, mathematics. E. Franckx is one of their number.The Instituto di Matematica Finanziaria of the University of Trieste (Faculty of Economics and Commerce) has published a booklet entitledEssai d'une théorie opérationnelle des risques Markoviens which contains three lectures delivered by Professor Franckx in Trieste and a contribution which he presented to the 17th Congress of Actuaries, held in London in 1964.

On the invariance principle for reversible Markov chains

2016 ◽  
Vol 53 (2) ◽  
pp. 593-599 ◽  
Author(s):  
Magda Peligrad ◽  
Sergey Utev
Keyword(s):  
Standard Deviation ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Markov Chains ◽  
Stochastic Processes ◽  
Partial Sums ◽  
Additive Functionals ◽  
Functional Clt ◽  
Reversible Markov Chains ◽  
Functional Central Limit

Abstract In this paper we investigate the functional central limit theorem (CLT) for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation of partial sums. For this case, we show that the functional CLT is equivalent to the fact that the variance of partial sums is regularly varying with exponent 1 and the partial sums satisfy the CLT. It is also equivalent to the conditional CLT.

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.

Aspiration-based Adaptive Rules

2011 ◽  
Author(s):  
Jonathan Bendor ◽  
Daniel Diermeier ◽  
David A. Siegel ◽  
Michael M. Ting
Keyword(s):  
Markov Chains ◽  
Stochastic Processes ◽  
Empirical Content ◽  
Qualitative Properties ◽  
Pareto Dominance ◽  
General Properties ◽  
And Performance

This chapter discusses some general properties of aspiration-based adaptive rules (ABARs). It begins with an overview of propensity and aspiration-based adjustment, using axioms to represent three premises: agents have aspirations, they compare payoffs to aspirations, and these comparisons determine the key qualitative properties of how agents adjust their action propensities. It then considers stochastic processes such as Markov chains before turning to some useful types of ABARs, along with realistic aspirations and how the behavior and performance of ABARs are associated with the existence of relations of Pareto dominance among alternatives. It also examines the empirical content of ABAR-driven models and concludes with an analysis of some evidence regarding aspiration-based adaptation, paying attention to behavior and hedonics.

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