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Introduction to Stochastic Processes, 2018
Markov chains are one of the most useful classes of stochastic processes, being • simple, flexible and supported by many elegant theoretical results • valuable for building intuition about random dynamic models • central to quantitative modeling in their
Gregory F. Lawler
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Markov chains are one of the most useful classes of stochastic processes, being • simple, flexible and supported by many elegant theoretical results • valuable for building intuition about random dynamic models • central to quantitative modeling in their
Gregory F. Lawler
semanticscholar +1 more source
The Evolution of Statistical Induction Heads: In-Context Learning Markov Chains
Neural Information Processing SystemsLarge language models have the ability to generate text that mimics patterns in their inputs. We introduce a simple Markov Chain sequence modeling task in order to study how this in-context learning (ICL) capability emerges.
Benjamin L. Edelman +4 more
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2005
Abstract Useful models of the real world have to satisfy two conflicting requirements: they must be sufficiently complicated to describe complex systems, but they must also be sufficiently simple for us to analyse them. This chapter introduces Markov chains, which have successfully modelled a huge range of scientific and social phenomena,
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Abstract Useful models of the real world have to satisfy two conflicting requirements: they must be sufficiently complicated to describe complex systems, but they must also be sufficiently simple for us to analyse them. This chapter introduces Markov chains, which have successfully modelled a huge range of scientific and social phenomena,
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1997
Markov chains are central to the understanding of random processes. This is not only because they pervade the applications of random processes, but also because one can calculate explicitly many quantities of interest. This textbook, aimed at advanced undergraduate or MSc students with some background in basic probability theory, focuses on Markov ...
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Markov chains are central to the understanding of random processes. This is not only because they pervade the applications of random processes, but also because one can calculate explicitly many quantities of interest. This textbook, aimed at advanced undergraduate or MSc students with some background in basic probability theory, focuses on Markov ...
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IEEE Trans. Inf. Theory, 1984
Summary: The Markov chain that has maximum entropy for given first and second moments is determined. The solution provides a discrete analog to the continuous Gauss-Markov process.
Jørn Justesen, Tom Høholdt
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Summary: The Markov chain that has maximum entropy for given first and second moments is determined. The solution provides a discrete analog to the continuous Gauss-Markov process.
Jørn Justesen, Tom Høholdt
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1992
Abstract In Section 7.3, we briefly introduced models for Markov chains in the simple case where there were only two possible responses: an event occurs or not. However, such models have much wider application. In continuous time models, where each subject is in one of several possible states at any given point, they are often called ...
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Abstract In Section 7.3, we briefly introduced models for Markov chains in the simple case where there were only two possible responses: an event occurs or not. However, such models have much wider application. In continuous time models, where each subject is in one of several possible states at any given point, they are often called ...
openaire +1 more source