Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Parrondo effect in correlated random walks with general jumps

일반 점프크기를 가지는 상관 확률보행의 파론도 효과

  • Lee, Jiyeon (Department of Statistics, Yeungnam University)
  • Received : 2016.08.11
  • Accepted : 2016.09.02
  • Published : 2016.09.30
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Abstract

We consider a correlated discrete-time random walk in which the current jump size depends on the previous jump size and a noncorrelated discrete-time random walk where the jump size is determined independently. By using the strong law of large numbers of Markov chains we derive the formula for the asymptotic means of the random mixture and the periodic pattern of these two random walks and then we show that there exists Parrondo's paradox where each random walk has mean 0 but their random mixture and periodic pattern have negative or positive means. We describe the parameter sets at which Parrondo's paradox holds in each case.

일정한 시간 간격으로 임의의 점프크기가 계속 누적되는 이산시간 확률보행을 고려한다. 각 시점에서의 점프크기가 이전 시점의 점프크기에 종속되어 결정되는 상관 확률보행과 각 시점에서의 점프크기가 이전 시점의 점프크기와 무관하게 독립적으로 결정되는 무상관 확률보행의 점근적 평균을 각각 계산한다. 그리고 상관 확률보행과 무상관 확률보행을 임의적으로 혼합하여 결합하거나 또는 일정한 패턴에 따라 주기적으로 반복하여 결합하는 혼합 확률보행의 점근적 평균 식을 유도한다. 각 확률보행의 점근적 평균은 0으로 공정한 게임을 나타내지만 두 확률보행을 결합한 혼합 확률보행의 점근적 평균은 음수가 되어 지는 게임이 되거나 또는 양수가 되어 이기는 게임이 되는 파론도 역설 현상이 나타남을 확인하고 해당되는 각 모수의 범위를 찾는다.

Keywords

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