# law of large numbers

### Law of Large Numbers

... Kljuˇ cne rijeˇ ci: Matematiˇ cko oˇ cekivanje, sluˇ cajna varijabla, mjera, vjerojatnost, niz, ko- nvergencija, red, nejednakost, nezavisnost, konstanta Abstract: In this paper we will talk about conditions in which ...

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### A Note on the Strong Law of Large Numbers

... Zygmund theorem for pairwise NQD random variables. 1 Introduction Let {X n , n ≥ 1} be a sequence of independent and identically dis- tributed random variables. There are two famous theorems on the strong law of ...

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### Section 7C: The Law of Large Numbers

... Section 7C: The Law of Large Numbers Example. You flip a coin 100 times. I Suppose the coin is fair. How many times would you expect to get heads? tails? One would expect a fair coin to come up heads ...

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### Purification, Saturation and the Exact Law of Large Numbers

... Exact law of large numbers · Fubini extension · Incomplete informa- tion · Purification · Saturated probability space ∗ The authors are very grateful to Yi-Chun Chen, Sengkee Chua, Haifeng Fu, ...

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### Characterization of risk: a sharp law of large numbers

... the law of large numbers when a large sample of agents is drawn at ...“sharp” law of large ...this law if and only if it is both Pettis-integrable and norm integrably ...

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### Strong Law of Large Numbers under an Upper Probability

... Strong law of large numbers is a fundamental theory in probability and ...this law is very different from additive ...strong law of large numbers under upper probability V ...

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### On Strong Law of Large Numbers for Dependent Random Variables

... We discuss strong law of large numbers and complete convergence for sums of uniformly bounded negatively associate NA random variables RVs. We extend and generalize some recent results. As ...

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### The Law of Large Numbers for self-exciting correlated defaults

... becomes large, showing that under some monotonicity conditions the limiting average loss process can be determined by a fixed point ...the Law of Large Numbers holds under certain ...

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### Doob's Type Inequality and Strong Law of Large Numbers for Demimartingales

... strong law of large numbers, strong growth rate, and integrability of supremum for demimartingales, which generalize and improve partial results of Christofides 2000 and Prakasa Rao 2007 ...

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### On conditions for the strong law of large numbers in general Banach spaces

... ANNA KUCZMASZEWSKA and DOMINIK SZYNAL (Received 4 August 1998 and in revised form 26 March 1999) Abstract. We give Chung-Teicher type conditions for the SLLN in general Banach spaces under the assumption that the weak ...

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### A LAW OF LARGE NUMBERS FOR FINITE-RANGE DEPENDENT RANDOM MATRICES

... A LAW OF LARGE NUMBERS FOR FINITE-RANGE DEPENDENT RANDOM MATRICES GREG ANDERSON AND OFER ZEITOUNI Abstract. We consider random hermitian matrices in which distant above- diagonal entries are ...

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### A law of large numbers for finite-range dependent random matrices

... makes the (unrealistic) assumption that gains between different pairs of antennas are uncorrelated. The models studied in this work would allow correlation between neighboring antenna pairs. We do not develop this ...

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### Not a fallacy of the law of large numbers : pooling risks and the utility of insurance

... Considering a sequence of independent and identically distributed (IID) replications of a gamble that is initially rejected, Samuelson (1963) famously demonstrates the “fallacy of large numbers” in a ...

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### Strong law of large numbers for countable nonhomogeneous Markov chains

... In this section, we shall establish the strong law of large numbers for countable nonhomogeneous Markov chains under the condition of uniform convergence in the Cesàro sense. The results obtained are ...

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### A Weighted Weak Law of Large Numbers for Free Random Variables

... The weak law of large numbers (WLLN) proved by Kolmogorov is one of the most beautiful results in classical probability theory. Quite recently, this funda- mental limit theorem was extended by ...

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### On the Convergence Rate of the Law of Large Numbers for Sums of Dependent Random Variables

... n → ∞ The question underlying the present work is how one may refine Theorem CG1 to give more information on the law of { X n } . We recall the classical answer, the strong law of large ...

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### On strong law of large numbers and growth rate for a class of random variables

... strong law of large numbers for a class of random variables satisfying the maximal moment inequality with exponent ...strong law of large numbers and the Marcinkiewicz strong ...

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### Chapter 6: Variance, the law of large numbers and the Monte-Carlo method

... The Law of Large numbers Suppose we perform an experiment and a measurement encoded in the random variable X and that we repeat this experiment n times each time in the same conditions and each time ...

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### The Strong Law of Large Numbers for U-Statistics under Random Censorship

... strong law of large numbers for the semiparametric U-statistics estimator S se 2,n , under proper conditions, has been established in Theorem ...especially large for smaller sample ...

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### Law of large numbers for non-elliptic random walks in dynamic random environments

... We prove a law of large numbers for a class of Z d -valued random walks in dynamic random environ- ments, including non-elliptic examples. We assume for the random environment a mixing property ...

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