Central limit theorem for a class of SPDEs

Fatheddin, Parisa

doi:10.1239/jap/1445543846

Cited by 6 publications

(3 citation statements)

References 25 publications

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“…Recently, numerous mathematicians work on central limit theorem (CLT); see, e.g., [21,18,33]. Since moderate deviation principle (MDP) fills the gap between CLT scale and LDP scale, it has been gained much attention.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Moderate deviation and central limit theorem for stochastic differential delay equations with polynomial growth

2018

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In this paper, employing the weak convergence method, based on a variational representation for expected values of positive functionals of a Brownian motion, we investigate moderate deviation for a class of stochastic differential delay equations with small noises, where the coefficients are allowed to be highly nonlinear growth with respect to the variables. Moreover, we obtain the central limit theorem for stochastic differential delay equations which the coefficients are polynomial growth with respect to the delay variables.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Moderate deviation and central limit theorem for stochastic differential delay equations with polynomial growth

2018

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“…This theorem provides an avenue to sample non-normally distributed populations with a guarantee of getting approximately the same results as would have been obtained if the population were normally distributed provided that sample size is large. However, for small sample sizes, the shape of the sampling distribution of mean is less than the parent population from which samples were drawn (Fatheddin, 2015). On the other hand, the shape looks more like a normal distribution as sample size gets larger.…”

Section: Central Limit Theorem (Clt)mentioning

confidence: 98%

Application of Three Probability Distributions to Justify Central Limit Theorem

I.,

C.O.,

C.O.

2023

African Journal of Mathematics and Statistics Studies

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This paper focused on the use of three probability distributions to justify the central limit theorem (CLT). The aim was to use the moment generating function (MGF) to prove (CLT) and also to portray the shape of different sample sizes (15, 30 and 100) of distributions of sample means on a histogram. The population distributions studied were: Normal, Gamma and Exponential distributions. In addition, sampling distribution of the mean table was constructed for better understanding of CLT. The study used simulation to simulate population distribution of Normal, Gamma and Exponential. Five hundred (500) distributions of sample means were drawn from each of the simulated population distributions at three different sample sizes (n): 15, 30 and 100. The shape of the simulated population distribution and sampling distribution of mean were presented on a histogram. The mean and standard deviation of each population distribution together with distribution of sample means at different sample sizes were also presented on the histogram plotted. The findings showed that under normal distribution, the sampling distribution of mean produced a shape like normal distribution irrespective of the sample size. Conversely, the shape of sampling distribution of mean under non-normal distributions gradually converges to normal distribution as sample size tends to infinity, while the variability of each sampling distribution decreases as the sample size increases. Therefore, CLT holds for large sample size (n ≥ 30).

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“…Among them are two of the most commonly studied population models, namely, super-Brownian motion (SBM) and the Fleming-Viot process (FVP). These population models have been the focus of numerous recent publications, among which is [6] in which the authors established the central limit theorem for the two models. One of the interesting problems for these models is to set the branching rate for SBM and a resampling rate for the FVP to tend to 0 and to study the rate at which the population's measure converges to a deterministic limit.…”

Section: Introductionmentioning

confidence: 99%