A Study On The Simple Random Walk


Abstract


An important class of Markov chain problems is the random walk problems. In a random walk the state of the Markov chain are the integers and the jumps of the chain from state are only to neighbor states . There are many variations on this basic design. When the state space of the chain is finite it is sometimes called the gamblers ruin problem. There are various martingale and Markov chain methods to analyze probabilistic characteristics of a simple random walk. In this study a simple random walk is defined and the first time that this random walk visits the state is analyzed by using generating functions. is calculated in terms of the probabilities and .


Keywords


Markov chain; random walk; generating functions.

Full Text:

PDF

References


Elena Kosygina, Martin P. W. Zerner. Excursions of excited random walks on integers, Electron J. Probab. (19) 2004, no 25, 1-25. ISSN: 1083-6489

Ratnadip Adhikari, R. K. Agrawal. A combination of artificial neural network and random walk models for financial time series forecasting, Neural Computing and Applications, May 2014, Volume 24, Issue 6, pp 14411449.

Alexandros B., Gareth R., Alexandre T. and Natesh P. Asymptotic Analysis of the Random-Walk Metropolis Algorithm on Ridged Densities, arXiv:1510.02577

Jiahan L., Ilias T., Wei W. Predicting Exchange Rates Out of Sample: Can Economic Fundamentals Beat the Random Walk?, Journal of Financial Econometrics (2015) 13 (2): 293-341.

Philip L. S., Roger R. Diffusion and Random Walk Processes, International Encyclopedia of the Social & Behavioral Sciences, 2nd edition, Vol 6. Oxford: Elsevier. pp. 395401. ISBN: 9780080970868.

Sidney, I. Resnick. Adventures in Stochastic Processes, Springer Science+Business Media, New York, 3rd printing, 2002.

H. Kobayashi, B. L. Mark, W. Turin. Probability, Random Processes and Statistical Analysis, Cambridge University Press, 2012.

G. Grimmett and D. Stirzaker, Probability and Random Processes, Oxford University Press, 2001.

W. J. Stewart, Probability, Markov Chains, Queues and Simulation: the Mathematical Basis of Performance Modeling, Princeton University Press, 2009.


Refbacks

  • There are currently no refbacks.


 

 
  
 

 

  


About IJSBAR | Privacy PolicyTerms & Conditions | Contact Us | DisclaimerFAQs 

IJSBAR is published by (GSSRR).