the central limit theorem

... ), and the theorem is proved , 30 Chapter Main Results In this chapter, we use the Stein’s method to bound the convergence rate in the central limit theorem for the total magnetization in the Curie-Weiss-Potts ... ITS APPLICATION 25 Then for W := Sn − nα , n1−1/2k we have for any l ∈ N E|W |l const.(l) In the following theorems, Theorem 3.4.3 is from [11], Theorem 3.4.4 is from [12], Theorem 3.4.5, Corollary ... exp[− Rq x, D2 Gβ (¯ ν )x + t, x ]dx We now prove the central limit theorem, that is, Theorem 2.2.11 CHAPTER THE CURIE-WEISS-POTTS MODEL 16 Proof of Theorem 2.2.11: According to Lemma 2.2.13 with...

Ngày tải lên: 03/10/2015, 21:57

... with the uniform distribution over Sn For a set S, the indicator function of S is denoted by 1(S) and the cardinal of S is denoted by |S| The following theorem will be proved in this note Theorem ... Subhankar Lp bounds for a central limit theorem with involutions Available at http://arxiv.org/abs/0905.1150 [7] Goldstein, Larry Berry-Esseen bounds for combinatorial central limit theorems and pattern ... bound for the remainder in a combinatorial central limit theorem Ann Probab (1978), no 2, 231–249 [11] Hoeffding, Wassily A combinatorial central limit theorem Ann Math Statist 22, (1951), 558–...

Ngày tải lên: 16/10/2015, 09:13

... note on the almost sure central limit theorem for the product of partial sums,” Applied Mathematics Letters, vol 19, pp 191–196, 2004 J S Jin, “An almost sure central limit theorem for the product ... “A note on the almost sure central limit theorem, ” Statistics & Probability Letters, vol 9, no 3, pp 201–205, 1990 M Peligrad and Q M Shao, “A note on the almost sure central limit theorem for ... almost sure central limit theory,” Stochastic Processes and a Their Applications, vol 94, no 1, pp 105–134, 2001 M Peligrad and S Utev, Central limit theorem for linear processes,” The Annals...

Ngày tải lên: 21/06/2014, 05:20

... everywhere central limit theorem, ” Mathematical Proceedings of the Cambridge Philosophical Society, vol 104, no 3, pp 561–574, 1988 P Schatte, “On strong versions of the central limit theorem, ” Mathematische ... Probability Letters, vol 76, no 11, pp 1175–1184, 2006 M Dudzinski, The almost sure central limit theorems in the joint version for the maxima and sums ´ of certain stationary Gaussian sequences,” ... obtain the desired result , i 1, 3.16 Journal of Inequalities and Applications Lemma 3.4 Let {Xn } be a sequence of standard Gaussian variables satisfying the conditions of Theorem 2.1, then for...

Ngày tải lên: 21/06/2014, 07:20

Ngày tải lên: 05/08/2014, 09:46

... in the renewal theory Applying Theorem 2.4 for the imbedded chain {(Zn , ρn ), n ≥ 1} we obtain the following theorem Theorem 3.2 (Central limit theorem for the imbedded chain) Assume that the ... we state and prove the main theorem as follows Central Limit Theorem for Functional of Jump Markov Processes 459 Theorem 3.3 Assume that the condition (C1 ) of Theorem 3.2 and the following condition ... section is to establish the conditions for n−1/2 n L ϕ(Xk ) −→ N (μ, σ ) k=1 We need a central limit theorem for martingale differences as follows Theorem 2.3 (Central limit theorem for martingale...

Ngày tải lên: 06/08/2014, 05:20

... the MP law is known as the standard MP law The following theorem extend the above result to the non-i.i.d case for sample covariance matrices proposed in Bai and Silverstein (2006, page 46) Theorem ... |x| ≤ 2σ; (2.2) otherwise The following theorem is the generalized result of the non-i.i.d case proved by Bai and Silverstein (2006, page 23) 16 Chapter 2: Literature Review Theorem 2.1.2 Suppose ... 1/y at the origin if y > 1, where a = σ2 (1 − σ2 (1 + √ y) and b = √ y) ; the constant y is the dimension to sample size ratio index The limiting distribution of Theorem 2.1.3 is called the Marˇ...

Ngày tải lên: 12/09/2015, 09:39

... M: On the convergence of generalized moments in almost sure central limit theorem Stat Probab Lett 40, 343–351 (1998) 11 [6] Miao, Y: Central limit theorem and almost sure central limit theorem ... Schatte, P: On strong versions of the central limit theorem Mathematische Nachrichten 137, 249–256 (1988) [4] Lacey, MT, Philipp, W: A note on the almost sure central limit theorem Statist Probab Lett ... I(|X| ≤ x) lim (2) In contrast to the well-known classical central limit theorem, Gine et al [1] obtained the following self-normalized d version of the central limit theorem: (S n − ES n )/Vn −→...

Ngày tải lên: 20/06/2014, 21:20

... is just the definition of IP , and the rest follows from the “standard f f machine” If A G and IP A = 0, then QA = 0, so I A = In other words, the measure I P P f The Radon-Nikodym theorem ... Theorem, continued) We show in Fig 9.1 the values of the martingale Zk We always have Z0 = 1, since Z0 = IEZ = Z e ZdIP = IP  = 1: 9.3 The State Price Density Process In order to express the ... -measurable, it is the conditional expectation (under the probability measure Q) of X given G The existence of conditional expectations is a consequence of the Radon-Nikodym theorem ...

Ngày tải lên: 18/10/2013, 03:20

... accessibility of the former within the framework of mean-field theory, as well as the finite connectivity of the latter Interest in these models has intensified lately since they occur in the context ... ‘energy’ states On the other hand, there is only one way of covering the graph with the + + + state, which of course corresponds to the global minimum of the ‘energy’ It is therefore more probable ... equilibrium at the dynamical transition temperature Furthermore, the energy will get stuck at the energy at which the transition occurs Since this phenomenon is the result of the drastic change in the geometry...

Ngày tải lên: 01/11/2013, 08:20

... compaction in the jamming limit, that the most compact configurations should be the most visited; and, on the other, the flatness hypothesis of Edwards, which states that for large enough systems, the macroscopic ... and the strict absence of one, the site n ‘looks like’ a point of perfect packing The grain at depth n then has the freedom to point the ‘wrong’ way; we call such sites excitations, using the thermal ... p(C) is the probability that the system is in the orientation configuration C in the steady state, and the sum runs over all the 2n configurations of a system of n grains This can be estimated theoretically...

Ngày tải lên: 01/11/2013, 08:20

Ngày tải lên: 17/12/2013, 15:19

... internal storage The CPU directs all the activities of the computer The control unit coordinates the sequencing of events within the processor The word” computer” usually refers to the CPU plus internal ... components The control unit directs the flow of information within the processor The arithmetic-logical unit of the processor is responsible for the interpretation of program instructions The arithmetic-logical ... III Locating information Find the passage in the text where the following ideas are expressed The processor is the control unit and the arithmetic-logical unit The processor operates on information...

Ngày tải lên: 21/12/2013, 20:15

... transcription together with the E2F site [20,21] The DRS ⁄ CHR in the B-Myb promoter deviates most from other CHR sequences with its two-nucleotide exchange from the CHR consensus (Fig 2) Changing the distance ... at the CDE ⁄ CHR It was shown that E2F4 binds to the CDE and that Lin-54 binds to the CHR in the Cdc2 promoter in G0 It is probable that these proteins constitute part of the DREAM complex on these ... one of them, the CDE in the mouse cyclin B2 promoter, is not perfectly conserved A one-nucleotide change is found in the human promoter The alteration appears to be sufficient to render the human...

Ngày tải lên: 16/02/2014, 09:20

... authority as the central bank The Bank of Canada is the central bank of Canada by that account The proposed usage comes from the literature on social networks In this literature, the highest ranked ... for the LVTS using the normalized BCL vectors for each bank This approach is based on the premise that money flows out of a bank in the proportions given by the BCLs the bank has with the other ... distribution of daily liquidity The bank with the highest value in the stationary vector is predicted to hold the most liquidity throughout the day and is thus the central bank An attractive feature...

Ngày tải lên: 16/02/2014, 12:20

... health risks; • the identification of all risk points along the chain of events from the origin of the wastewater to the consumption of the produce (e.g the farm-to-fork approach of the HAPPC method ... 2006 Figure 7: Looking at the costs and benefits, centralized systems may not be the answer in terms of best result for the investment The chart on the left shows that the financial NPV does not ... towards the sanitation target is off track 41 Regionally, there are large variations in progress towards this MDG For sanitation, the regions of Africa south of the Sahara and southern Asia show the...

Ngày tải lên: 17/02/2014, 10:20

... Although the European Union banned the pesticide in 2004, atrazine is still widely used in the United States The U.S Environmental Protection Agency (EPA) regulates the use of atrazine as well as the ... for the first time the results of surface water and drinking water monitoring required by the EPA across the Midwestern and Southern United States NRDC obtained these data from the EPA’s Ecological ... not incorporated into the determination of the level of concern associated with the contamination in the watershed In addition, the U.S Fish and Wildlife Service criticized the model for incorrectly...

Ngày tải lên: 15/03/2014, 10:20

... preferences for central banks of Japan, the UK and the U.S after the first oil shock The author showed that these countries increased their aversion to inflation volatility, especially from the 1980s ... that the current inflation rate depends on its lagged values, on the fluctuation of the exchange rate in the previous period and on the two-period lag of the output gap The verticality of the ... in the loss function of the central bank that minimizes the squared deviation between the actual interest rate and the optimal interest rate The optimal interest rate is derived based on the...

Ngày tải lên: 15/03/2014, 14:20

... irrespective of the amount of the loan However, the larger the loan, the larger the amount of the repayment installment, and a large installment may strain the repayment capacity of the borrower ... is due There has, therefore, to be a linkage between the amount of the loan and the tenure of the loan It is, therefore, suggested that for loans not exceeding Rs 15,000, the tenure of the loan ... sanctioning the credit facility In the case of securitized loans, banks are the owners of the loans and the MFIs are their agents for recovery They can therefore be considered as responsible for the...

Ngày tải lên: 15/03/2014, 14:20

... percent Increase the limit to 15 percent Feb-08 Increase the limit to 16 percent Jan-08 Increase the limit to 17 percent Apr-08 Increase the limit to 20 percent Oct-09 Increase the limit to 22 percent ... percent Jan-10 Increase the limit to 24 percent Jun-10 Increase the limit to 26 percent Jul-10 Increase the limit to 28 percent Sep-10 Increase the limit to 30 percent Jun-10 Limits to foreign currency ... position: raising the solvency of the 15% of capital financial system Increase the limit from 10.5 percent Reduce the appreciation to 12 percent of the domestic currency Increase the limit to 13.5...

Ngày tải lên: 15/03/2014, 14:20