Monte Carlo Methods and Applications最新文献_第4页

Monte Carlo method for parabolic equations involving fractional Laplacian 包含分数阶拉普拉斯式的抛物方程的蒙特卡罗方法

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Monte Carlo Methods and Applications Pub Date : 2022-10-27 DOI: 10.1515/mcma-2022-2129

Caiyu Jiao, Changpin Li

引用次数: 0

A random walk algorithm to estimate a lower bound of the star discrepancy 一种估计星差下界的随机游动算法

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Monte Carlo Methods and Applications Pub Date : 2022-10-21 DOI: 10.1515/mcma-2022-2125

Maryam Alsolami, M. Mascagni

{"title":"A random walk algorithm to estimate a lower bound of the star discrepancy","authors":"Maryam Alsolami, M. Mascagni","doi":"10.1515/mcma-2022-2125","DOIUrl":"https://doi.org/10.1515/mcma-2022-2125","url":null,"abstract":"Abstract In many Monte Carlo applications, one can substitute the use of pseudorandom numbers with quasirandom numbers and achieve improved convergence. This is because quasirandom numbers are more uniform that pseudorandom numbers. The most common measure of that uniformity is the star discrepancy. Moreover, the main error bound in quasi-Monte Carlo methods, called the Koksma–Hlawka inequality, has the star discrepancy in the formulation. A difficulty with this bound is that computing the star discrepancy is very costly. The star discrepancy can be computed by evaluating a function called the local discrepancy at a number of points. The supremum of these local discrepancy values is the star discrepancy. If we have a point set in [ 0 , 1 ] s {[0,1]^{s}} with N members, we need to compute the local discrepancy at N s {N^{s}} points. In fact, computing star discrepancy is NP-hard. In this paper, we will consider an approximate algorithm for a lower bound on the star discrepancy based on using a random walk through some of the N s {N^{s}} points. This approximation is much less expensive that computing the star discrepancy, but still accurate enough to provide information on convergence. Our numerical results show that the random walk algorithm has the same convergence rate as the Monte Carlo method, which is O ( N - 1 2 {O(N^{-frac{1}{2}}} ).","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"28 1","pages":"341 - 348"},"PeriodicalIF":0.9,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41818243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Superposition of forward and backward motion 前后运动叠加

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Monte Carlo Methods and Applications Pub Date : 2022-10-19 DOI: 10.1515/mcma-2022-2124

Manfred Harringer

引用次数: 1

Estimation of entropy and extropy based on right censored data: A Bayesian non-parametric approach 基于右截尾数据的熵和熵估计:一种贝叶斯非参数方法

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Monte Carlo Methods and Applications Pub Date : 2022-09-30 DOI: 10.1515/mcma-2022-2123

L. Al-Labadi, Muhammad Tahir

引用次数: 0

On the practical point of view of option pricing 论期权定价的实用观点

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Monte Carlo Methods and Applications Pub Date : 2022-09-28 DOI: 10.1515/mcma-2022-2122

N. Halidias

{"title":"On the practical point of view of option pricing","authors":"N. Halidias","doi":"10.1515/mcma-2022-2122","DOIUrl":"https://doi.org/10.1515/mcma-2022-2122","url":null,"abstract":"Abstract In this note, we describe a new approach to the option pricing problem by introducing the notion of the safe (and acceptable) price for the writer of an option, in contrast to the fair price used in the Black–Scholes model. Our starting point is that the option pricing problem is closely related with the hedging problem by practical techniques. Recalling that the Black–Scholes model does not give us the price of the option but the initial value of a replicating portfolio, we observe easily that this has a serious disadvantage because it assumes the building of this replicating portfolio continuously in time, and this is a disadvantage of any model that assumes such a construction. Here we study the problem from the practical point of view concerning mainly the over-the-counter market. This approach is not affected by the number of the underlying assets and is particularly useful for incomplete markets. In the usual Black–Scholes or binomial approach or some other approaches, one assumes that one can invest or borrow at the same risk-free rate r > 0 r>0 , which is not true in general. Even if this is the case, one can immediately observe that this risk-free rate is not a universal constant but is different among different people or institutions. So the fair price of an option is not so much fair! Moreover, the two sides are not, in general, equivalent against the risk; therefore, the notion of a fair price has no meaning at all. We also define a variant of the usual binomial model, by estimating safe upward and downward rates u , d u,d , trying to give a cheaper safe or acceptable price for the option.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"28 1","pages":"307 - 318"},"PeriodicalIF":0.9,"publicationDate":"2022-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46929711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Monte Carlo simulation of sensitivity functions for few-view computed tomography of strongly absorbing media 强吸收介质少视点计算机断层扫描灵敏度函数的蒙特卡罗模拟

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Monte Carlo Methods and Applications Pub Date : 2022-08-25 DOI: 10.1515/mcma-2022-2120

A. Konovalov, V. Vlasov, S. Kolchugin, G. Malyshkin, R. Mukhamadiyev

引用次数: 0

Scrambling additive lagged-Fibonacci generators 置乱加性滞后斐波那契生成器

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Monte Carlo Methods and Applications Pub Date : 2022-08-04 DOI: 10.1515/mcma-2022-2115

Haifa Aldossari, M. Mascagni

{"title":"Scrambling additive lagged-Fibonacci generators","authors":"Haifa Aldossari, M. Mascagni","doi":"10.1515/mcma-2022-2115","DOIUrl":"https://doi.org/10.1515/mcma-2022-2115","url":null,"abstract":"Abstract Random numbers are used in a variety of applications including simulation, sampling, and cryptography. Fortunately, there exist many well-established methods of random number generation. An example of a well-known pseudorandom number generator is the lagged-Fibonacci generator (LFG). Marsaglia showed that the lagged-Fibonacci generator using addition failed some of his DIEHARD statistical tests, while it passed all when longer lags were used. This paper presents a scrambler that takes bits from a pseudorandom number generator and outputs (hopefully) improved pseudorandom numbers. The scrambler is based on a modified Feistel function, a method used in the generation of cryptographic random numbers, and multiplication by a chosen multiplier. We show that this scrambler improves the quality of pseudorandom numbers by applying it to the additive LFG with small lags. The scrambler performs well based on its performance with the TestU01 suite of randomness tests. The TestU01 suite of randomness tests is more comprehensive than the DIEHARD tests. In fact, the specific suite of tests we used from TestU01 includes the DIEHARD tests The scrambling of the LFG is so successful that scrambled LFGs with small lags perform as well as unscrambled LFGs with long lags. This comes at the cost of a doubling of execution time, and provides users with generators with small memory footprints that can provide parallel generators like the LFGs in the SPRNG parallel random number generation package.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"28 1","pages":"199 - 210"},"PeriodicalIF":0.9,"publicationDate":"2022-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46604130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Standard deviation estimation from sums of unequal size samples 不等大小样本和的标准差估计

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Monte Carlo Methods and Applications Pub Date : 2022-08-04 DOI: 10.1515/mcma-2022-2118

M. Casquilho, J. Buescu

{"title":"Standard deviation estimation from sums of unequal size samples","authors":"M. Casquilho, J. Buescu","doi":"10.1515/mcma-2022-2118","DOIUrl":"https://doi.org/10.1515/mcma-2022-2118","url":null,"abstract":"Abstract In numerous industrial and related activities, the sums of the values of, frequently, unequal size samples are systematically recorded, for several purposes such as legal or quality control reasons. For the typical case where the individual values are not or no longer known, we address the point estimation, with confidence intervals, of the standard deviation (and mean) of the individual items, from those sums alone. The estimation may be useful also to corroborate estimates from previous statistical process control. An everyday case of a sum is the total weight of a set of items, such as a load of bags on a truck, which is used illustratively. For the parameters mean and standard deviation of the distribution, assumed Gaussian, we derive point estimates, which lead to weighted statistics, and we derive confidence intervals. For the latter, starting with a tentative reduction to equal size samples, we arrive at a solid conjecture for the mean, and a proposal for the standard deviation. All results are verifiable by direct computation or by simulation in a general and effective way. These computations can be run on public web pages of ours, namely for possible industrial use.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"28 1","pages":"235 - 253"},"PeriodicalIF":0.9,"publicationDate":"2022-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45218319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Simulation of transient and spatial structure of the radiative flux produced by multiple recombinations of excitons 激子多次重组产生的辐射通量的瞬态和空间结构的模拟

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Monte Carlo Methods and Applications Pub Date : 2022-08-04 DOI: 10.1515/mcma-2022-2117

K. Sabelfeld, V. Sapozhnikov

引用次数: 0

Approximate bounding of mixing time for multiple-step Gibbs samplers 多阶Gibbs采样器混合时间的近似边界

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Monte Carlo Methods and Applications Pub Date : 2022-08-04 DOI: 10.1515/mcma-2022-2119

David A. Spade

引用次数: 1