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On the maximal gain over head runs. / Frolov, A.; Martikainen, A.; Steinebach, J.

In: Studia Scientiarum Mathematicarum Hungarica, Vol. 34, No. 1-3, 1998, p. 165-181.

Research output: Contribution to journal › Article › peer-review

Harvard

Frolov, A, Martikainen, A & Steinebach, J 1998, 'On the maximal gain over head runs', Studia Scientiarum Mathematicarum Hungarica, vol. 34, no. 1-3, pp. 165-181.

APA

Frolov, A., Martikainen, A., & Steinebach, J. (1998). On the maximal gain over head runs. Studia Scientiarum Mathematicarum Hungarica, 34(1-3), 165-181.

Vancouver

Frolov A, Martikainen A, Steinebach J. On the maximal gain over head runs. Studia Scientiarum Mathematicarum Hungarica. 1998;34(1-3):165-181.

Author

Frolov, A. ; Martikainen, A. ; Steinebach, J. / On the maximal gain over head runs. In: Studia Scientiarum Mathematicarum Hungarica. 1998 ; Vol. 34, No. 1-3. pp. 165-181.

BibTeX

@article{65cca25210e342fbb3b6d977633a15b0,

title = "On the maximal gain over head runs",

abstract = "Let (Xi{"}, Yi) be a sequence of i.i.cl. random vectors where {Xi} are gains and {Yi} are indicators of successes in repetitions of a game of heads and tails. Put, S0 = 0, Sk = X1+ ⋯ + Xk, and let I{.} denote the indicator function of the event in brackets. Then MN = Max0≦l (Sm - Sl+1) I{Yl+1N = ⋯ = Ym = 1} is the maximal gain over sequences of successes without interruptions ({"}head runs{"}). We derive necessary and sufficient conditions for strong laws of large numbers for MN and find rates of convergence in these laws.",

keywords = "Convergence rate, Head run, Increment of random walk, Large deviations, Strong law of large numbers",

author = "A. Frolov and A. Martikainen and J. Steinebach",

year = "1998",

language = "English",

volume = "34",

pages = "165--181",

journal = "Studia Scientiarum Mathematicarum Hungarica",

issn = "0081-6906",

publisher = "Akademiai Kiado",

number = "1-3",

}

RIS

TY - JOUR

T1 - On the maximal gain over head runs

AU - Frolov, A.

AU - Martikainen, A.

AU - Steinebach, J.

PY - 1998

Y1 - 1998

N2 - Let (Xi", Yi) be a sequence of i.i.cl. random vectors where {Xi} are gains and {Yi} are indicators of successes in repetitions of a game of heads and tails. Put, S0 = 0, Sk = X1+ ⋯ + Xk, and let I{.} denote the indicator function of the event in brackets. Then MN = Max0≦l (Sm - Sl+1) I{Yl+1N = ⋯ = Ym = 1} is the maximal gain over sequences of successes without interruptions ("head runs"). We derive necessary and sufficient conditions for strong laws of large numbers for MN and find rates of convergence in these laws.

AB - Let (Xi", Yi) be a sequence of i.i.cl. random vectors where {Xi} are gains and {Yi} are indicators of successes in repetitions of a game of heads and tails. Put, S0 = 0, Sk = X1+ ⋯ + Xk, and let I{.} denote the indicator function of the event in brackets. Then MN = Max0≦l (Sm - Sl+1) I{Yl+1N = ⋯ = Ym = 1} is the maximal gain over sequences of successes without interruptions ("head runs"). We derive necessary and sufficient conditions for strong laws of large numbers for MN and find rates of convergence in these laws.

KW - Convergence rate

KW - Head run

KW - Increment of random walk

KW - Large deviations

KW - Strong law of large numbers

UR - http://www.scopus.com/inward/record.url?scp=0345201977&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0345201977

VL - 34

SP - 165

EP - 181

JO - Studia Scientiarum Mathematicarum Hungarica

JF - Studia Scientiarum Mathematicarum Hungarica

SN - 0081-6906

IS - 1-3

ER -

ID: 75020618