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Martingales

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Book cover Essentials of Stochastic Processes

Part of the book series: Springer Texts in Statistics ((STS))

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Abstract

In this chapter we will introduce a class of process that can be thought of as the fortune of a gambler betting on a fair game. These results will be important when we consider applications to finance in the next chapter. In addition, they will allow us to give more transparent proofs of some facts from Chap. 1 concerning exit distributions and exit times for Markov chains.

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References

  1. Athreya KB, Ney PE (1972) Branching processes. Springer, New York

    Book  MATH  Google Scholar 

  2. Geman S, Geman D (1984) Stochastic relaxation, gibbs distributions and the bayesian restoration ofimages. IEEE Trans Pattern Anal Mach Intell 6:721–741

    Article  MATH  Google Scholar 

  3. Gliovich T, Vallone R, Tversky A (1985) The hot hand in basketball: on the misperception of random sequences. Cogn Psychol 17:295–314

    Article  Google Scholar 

  4. Hammersley JM, D C Handscomb DC (1984) Monte Carlo methods. Chapman and Hall, London

    Google Scholar 

  5. Hastings WK (1970) Monte carlo sampling methods using markov chains and their applications. Biometrika 57:97–109

    Article  MathSciNet  MATH  Google Scholar 

  6. Kesten H, Stigum B (1966) A limit theorem for multi-dimensional galton-watson processes. Ann Math Stat 37:1211–1223

    Article  MATH  Google Scholar 

  7. Kirkpatrick S, Gelatt CD Jr, Vecchi M (1983) Optimizing by simulated annealing. Science 220:671–680

    Article  MathSciNet  MATH  Google Scholar 

  8. Metropolis N, Rosenbluth A, Rosenbluth M, Teller A, Teller E (1953) Equation of state computation by fast computing machines. J Chem Phys 21:1087–1092

    Article  Google Scholar 

  9. Tierney L (1994) Markov chains for exploring posterior distributions. Ann Stat 22:1701–1762

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Duke University, 90320, Durham, North Carolina, USA

    Richard Durrett

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  1. Richard Durrett
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© 2012 Springer Science+Business Media, LLC

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Durrett, R. (2012). Martingales. In: Essentials of Stochastic Processes. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3615-7_5

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