Stochastic processes with memory

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SUMMARY

This discussion focuses on stochastic processes with memory, specifically those where future states depend on past states. Participants reference modified Markov chains and long-range dependence as key concepts. Notable resources include a paper on long-range dependence from Cornell University and a comprehensive article available on arXiv. The consensus is that most literature on these topics is found in academic journals rather than textbooks.

PREREQUISITES
  • Understanding of stochastic processes
  • Familiarity with Markov chains
  • Knowledge of long-range dependence concepts
  • Access to academic journals for research
NEXT STEPS
  • Research modified Markov chains and their applications in finance
  • Explore long-range dependence in stochastic processes
  • Review academic journals for papers on memory-dependent stochastic processes
  • Examine the implications of memory in predictive modeling
USEFUL FOR

Researchers, mathematicians, and financial analysts interested in advanced stochastic modeling and the implications of memory in predictive systems.

copernicus1
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Can anyone provide references for stochastic processes where future steps do depend on the past state of the system? Most of the material I'm finding deals purely with memoryless processes. Thanks!
 
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http://arxiv.org/ftp/math/papers/0401/0401144.pdf

There's one article I kept in my bookmarks. In fact, if you're interested, many papers on modified markov chains that take past state of the system in account for either short or long term duration will end up being financial in nature.

http://legacy.orie.cornell.edu/gennady/techreports/LRD-NOW.pdf

Here's a paper on long range dependence. It'll be a bit tough to actually find a textbook type reference for these topics though. I've only encountered them in journals.
 
Thanks!
 

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