Pub Date : 2022-11-07DOI: 10.1137/s0040585x97t991027
C. Lu, W. Yu, R. L. Ji, H. L. Zhou, X. J. Wang
Theory of Probability &Its Applications, Volume 67, Issue 3, Page 415-433, November 2022. Recently, Wang and Hu [Theory Probab. Appl., 63 (2019), pp. 479--499] established the Berry--Esseen bounds for $rho$-mixing random variables (r.v.'s) with the rate of normal approximation $O(n^{-1/6}log n)$ by using the martingale method. In this paper, we establish some general results on the rates of normal approximation, which include the corresponding ones of Wang and Hu. The rate can be as high as $O(n^{-1/5})$ or $O(n^{-1/4}log^{1/2} n)$ under some suitable conditions. As applications, we obtain the Berry--Esseen bounds of sample quantiles based on $rho$-mixing random samples. Finally, we also present some numerical simulations to demonstrate finite sample performances of the theoretical result.
概率论及其应用，第67卷，第3期，第415-433页，2022年11月。最近，王和胡[理论概率。苹果。[j]， 63 (2019)， pp. 479—499]通过使用鞅方法建立了$rho$ -混合随机变量(r.v.s)的Berry—Esseen界，其正态逼近率为$O(n^{-1/6}log n)$。本文建立了一些关于正态逼近速率的一般结果，其中包括Wang和Hu的相应结果。在适当的条件下，速率可高达$O(n^{-1/5})$或$O(n^{-1/4}log^{1/2} n)$。作为应用，我们得到了基于$rho$混合随机样本的样本分位数的Berry—Esseen界。最后，通过数值模拟验证了理论结果的有限样本性能。
{"title":"A Note on the Berry--Esseen Bounds for $rho$-Mixing Random Variables and Their Applications","authors":"C. Lu, W. Yu, R. L. Ji, H. L. Zhou, X. J. Wang","doi":"10.1137/s0040585x97t991027","DOIUrl":"https://doi.org/10.1137/s0040585x97t991027","url":null,"abstract":"Theory of Probability &Its Applications, Volume 67, Issue 3, Page 415-433, November 2022. <br/> Recently, Wang and Hu [Theory Probab. Appl., 63 (2019), pp. 479--499] established the Berry--Esseen bounds for $rho$-mixing random variables (r.v.'s) with the rate of normal approximation $O(n^{-1/6}log n)$ by using the martingale method. In this paper, we establish some general results on the rates of normal approximation, which include the corresponding ones of Wang and Hu. The rate can be as high as $O(n^{-1/5})$ or $O(n^{-1/4}log^{1/2} n)$ under some suitable conditions. As applications, we obtain the Berry--Esseen bounds of sample quantiles based on $rho$-mixing random samples. Finally, we also present some numerical simulations to demonstrate finite sample performances of the theoretical result.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"59 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-07DOI: 10.1137/s0040585x97t991039
T. C. Son, L. V. Dung, D. T. Dat, T. T. Trang
Theory of Probability &Its Applications, Volume 67, Issue 3, Page 434-451, November 2022. The aim of this paper is to apply the theory of regularly varying functions for studying Marcinkiewicz weak and strong laws of large numbers for the weighted sum $S_n=sum_{j=1}^{m_n}c_{nj}X_j$, where $(X_n;, ngeq 1)$ is a sequence of dependent random vectors in Hilbert spaces, and $(c_{nj})$ is an array of real numbers. Moreover, these results are applied to obtain some results on the convergence of multivariate Pareto--Zipf distributions and multivariate log-gamma distributions.
{"title":"Generalized Marcinkiewicz Laws for Weighted Dependent Random Vectors in Hilbert Spaces","authors":"T. C. Son, L. V. Dung, D. T. Dat, T. T. Trang","doi":"10.1137/s0040585x97t991039","DOIUrl":"https://doi.org/10.1137/s0040585x97t991039","url":null,"abstract":"Theory of Probability &Its Applications, Volume 67, Issue 3, Page 434-451, November 2022. <br/> The aim of this paper is to apply the theory of regularly varying functions for studying Marcinkiewicz weak and strong laws of large numbers for the weighted sum $S_n=sum_{j=1}^{m_n}c_{nj}X_j$, where $(X_n;, ngeq 1)$ is a sequence of dependent random vectors in Hilbert spaces, and $(c_{nj})$ is an array of real numbers. Moreover, these results are applied to obtain some results on the convergence of multivariate Pareto--Zipf distributions and multivariate log-gamma distributions.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"24 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-07DOI: 10.1137/s0040585x97t991015
M. Biret, M. Broniatowski, Z. Cao
Theory of Probability &Its Applications, Volume 67, Issue 3, Page 389-414, November 2022. We explore some properties of the conditional distribution of an independently and identically distributed (i.i.d.) sample under large exceedances of its sum. Thresholds for the asymptotic independence of the summands are observed, in contrast with the classical case when the conditioning event is in the range of a large deviation. This paper is an extension of Broniatowski and Cao [Extremes, 17 (2014), pp. 305--336]. Tools include a new Edgeworth expansion adapted to specific triangular arrays, where the rows are generated by tilted distribution with diverging parameters, and some Abelian type results.
概率论及其应用，67卷，第3期，389-414页，2022年11月。研究了独立同分布(i.i.d)样本在其和的大超出下的条件分布的一些性质。与经典情况相比，当条件作用事件在较大偏差范围内时，观察到求和的渐近独立性的阈值。本文是Broniatowski和Cao [Extremes, 17 (2014)， pp. 305—336]的延伸。工具包括一个新的Edgeworth扩展，适用于特定的三角形数组，其中行是由具有发散参数的倾斜分布产生的，以及一些阿贝尔类型的结果。
{"title":"A Gibbs Conditional Theorem under Extreme Deviation","authors":"M. Biret, M. Broniatowski, Z. Cao","doi":"10.1137/s0040585x97t991015","DOIUrl":"https://doi.org/10.1137/s0040585x97t991015","url":null,"abstract":"Theory of Probability &Its Applications, Volume 67, Issue 3, Page 389-414, November 2022. <br/> We explore some properties of the conditional distribution of an independently and identically distributed (i.i.d.) sample under large exceedances of its sum. Thresholds for the asymptotic independence of the summands are observed, in contrast with the classical case when the conditioning event is in the range of a large deviation. This paper is an extension of Broniatowski and Cao [Extremes, 17 (2014), pp. 305--336]. Tools include a new Edgeworth expansion adapted to specific triangular arrays, where the rows are generated by tilted distribution with diverging parameters, and some Abelian type results.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"13 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-20DOI: 10.3760/cma.j.cn501120-20210122-00032
B Q Liu, D S Dong, M Y Shi, W Zhang, W Wang, Y C Chen
Objective: To investigate the clinical effects of en bloc resection and debridement combined with gluteus maximus muscle flap in the treatment of ischial tubercle pressure ulcer complicated with chronic osteomyelitis. Methods: A retrospective observational study was conducted. From May 2018 to February 2020, 8 patients with pressure ulcers on the ischial tuberosity combined with chronic osteomyelitis who met the inclusion criteria were admitted to Fuyang Minsheng Hospital, including 5 males and 3 females, aged 38-69 years, with unilateral lesions in 6 patients and bilateral lesions in 2 patients. According to the anatomical classification of Cierny-Mader osteomyelitis, there were 6 patients (7 sides) with focal type, and 2 patients (3 sides) with diffuse type. The wound areas were 3 cm×2 cm to 12 cm×9 cm on admission. The pressure ulcer and chronic osteomyelitis lesions were completely removed by en bloc resection and debridement. The chronic infectious lesions were transformed into sterile incisions like fresh wounds by one surgical procedure, and the gluteus maximus muscle flaps with areas of 10 cm×6 cm to 15 cm×9 cm were excised to transfer and fill the ineffective cavity. The wounds of 5 patients were sutured directly, and the wounds of 3 patients were closed by local flap transfer. The intraoperative blood loss volume and blood transfusion, and length of hospital stay of patients were recorded. The incision healing and flap survival of patients were observed after operation. The recurrence of pressure ulcer and osteomyelitis, the appearance of the affected area, and the secondary dysfunction and deformity of the muscle flap donor site of patients were observed during followed up. Results: The intraoperative blood loss volume of the 8 patients was 220 to 900 (430±150) mL; 5 patients received intraoperative blood transfusion, of which 2 patients received 3 U suspended red blood cells and 3 patients received 2 U suspended red blood cells. The length of hospital stay was 18 to 29 (23.5±2.0) d for the 8 patients. In this group of patients, the incisions of 7 patients healed, while in one case, the incision suture was torn off during turning over and healed after secondary suture. The flaps survived well in 3 patients who underwent local flap transfer. During the follow-up period of 6-20 months, no recurrence of pressure ulcer or osteomyelitis occurred in 8 patients, the affected part had skin with good texture, mild pigmentation, and no sinus tract formation, and no secondary dysfunction or deformity occurred in the donor site. Conclusions: The en bloc resection and debridement combined with gluteus maximus muscle flap has good clinical effects on ischial tubercle pressure ulcer complicated with chronic osteomyelitis. Neither pressure ulcer nor osteomyelitis recurs post operation. The skin texture and appearance of the affected area are good, and the donor site has no secondary dysfunction or deformity.
{"title":"[Clinical effects of en bloc resection and debridement combined with gluteus maximus muscle flap in the treatment of ischial tubercle pressure ulcer complicated with chronic osteomyelitis].","authors":"B Q Liu, D S Dong, M Y Shi, W Zhang, W Wang, Y C Chen","doi":"10.3760/cma.j.cn501120-20210122-00032","DOIUrl":"10.3760/cma.j.cn501120-20210122-00032","url":null,"abstract":"<p><p><b>Objective:</b> To investigate the clinical effects of en bloc resection and debridement combined with gluteus maximus muscle flap in the treatment of ischial tubercle pressure ulcer complicated with chronic osteomyelitis. <b>Methods:</b> A retrospective observational study was conducted. From May 2018 to February 2020, 8 patients with pressure ulcers on the ischial tuberosity combined with chronic osteomyelitis who met the inclusion criteria were admitted to Fuyang Minsheng Hospital, including 5 males and 3 females, aged 38-69 years, with unilateral lesions in 6 patients and bilateral lesions in 2 patients. According to the anatomical classification of Cierny-Mader osteomyelitis, there were 6 patients (7 sides) with focal type, and 2 patients (3 sides) with diffuse type. The wound areas were 3 cm×2 cm to 12 cm×9 cm on admission. The pressure ulcer and chronic osteomyelitis lesions were completely removed by en bloc resection and debridement. The chronic infectious lesions were transformed into sterile incisions like fresh wounds by one surgical procedure, and the gluteus maximus muscle flaps with areas of 10 cm×6 cm to 15 cm×9 cm were excised to transfer and fill the ineffective cavity. The wounds of 5 patients were sutured directly, and the wounds of 3 patients were closed by local flap transfer. The intraoperative blood loss volume and blood transfusion, and length of hospital stay of patients were recorded. The incision healing and flap survival of patients were observed after operation. The recurrence of pressure ulcer and osteomyelitis, the appearance of the affected area, and the secondary dysfunction and deformity of the muscle flap donor site of patients were observed during followed up. <b>Results:</b> The intraoperative blood loss volume of the 8 patients was 220 to 900 (430±150) mL; 5 patients received intraoperative blood transfusion, of which 2 patients received 3 U suspended red blood cells and 3 patients received 2 U suspended red blood cells. The length of hospital stay was 18 to 29 (23.5±2.0) d for the 8 patients. In this group of patients, the incisions of 7 patients healed, while in one case, the incision suture was torn off during turning over and healed after secondary suture. The flaps survived well in 3 patients who underwent local flap transfer. During the follow-up period of 6-20 months, no recurrence of pressure ulcer or osteomyelitis occurred in 8 patients, the affected part had skin with good texture, mild pigmentation, and no sinus tract formation, and no secondary dysfunction or deformity occurred in the donor site. <b>Conclusions:</b> The en bloc resection and debridement combined with gluteus maximus muscle flap has good clinical effects on ischial tubercle pressure ulcer complicated with chronic osteomyelitis. Neither pressure ulcer nor osteomyelitis recurs post operation. The skin texture and appearance of the affected area are good, and the donor site has no secondary dysfunction or deformity.</p>","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"53 1","pages":"363-368"},"PeriodicalIF":0.0,"publicationDate":"2022-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86462663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"QuickStats: Rate* of Deaths Attributed to Unintentional Injury from Fire or Flames,† by Sex and Urban-Rural Status§ - National Vital Statistics System, United States, 2020.","authors":"","doi":"10.15585/mmwr.mm7114a5","DOIUrl":"10.15585/mmwr.mm7114a5","url":null,"abstract":"","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"58 1","pages":"529"},"PeriodicalIF":33.9,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8989375/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86474487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1137/s0040585x97t990617
V. Bogachev
{"title":"Chebyshev--Hermite Polynomials and Distributions of Polynomials in Gaussian Random Variables","authors":"V. Bogachev","doi":"10.1137/s0040585x97t990617","DOIUrl":"https://doi.org/10.1137/s0040585x97t990617","url":null,"abstract":"","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"2 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74410708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1137/s0040585x97t990654
A. Barrasso, N. Touzi
Рассматривается игра среднего поля с одним внешним шумом, коэффициент диффузии которого включает управление. Доказывается существование слабого решения с релаксацией при некоторых условиях на коэффициент диффузии. Далее, показывается, что при отсутствии этого внешнего шума игра среднего поля описывается обратным стохастическим дифференциальным уравнением типа Маккина–Власова второго порядка.
{"title":"Controlled Diffusion Mean Field Games with Common Noise and McKean--Vlasov Second Order Backward SDEs","authors":"A. Barrasso, N. Touzi","doi":"10.1137/s0040585x97t990654","DOIUrl":"https://doi.org/10.1137/s0040585x97t990654","url":null,"abstract":"Рассматривается игра среднего поля с одним внешним шумом, коэффициент диффузии которого включает управление. Доказывается существование слабого решения с релаксацией при некоторых условиях на коэффициент диффузии. Далее, показывается, что при отсутствии этого внешнего шума игра среднего поля описывается обратным стохастическим дифференциальным уравнением типа Маккина–Власова второго порядка.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"50 1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77777471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1137/s0040585x97t990642
N. Agram, S. Haadem, B. Øksendal, F. Proske
{"title":"Optimal Stopping, Randomized Stopping, and Singular Control with General Information Flow","authors":"N. Agram, S. Haadem, B. Øksendal, F. Proske","doi":"10.1137/s0040585x97t990642","DOIUrl":"https://doi.org/10.1137/s0040585x97t990642","url":null,"abstract":"","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"7 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88767174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1137/s0040585x97t990605
S. G. Bobkov, V. Ulyanov
{"title":"The Chebyshev--Edgeworth Correction in the Central Limit Theorem for Integer-Valued Independent Summands","authors":"S. G. Bobkov, V. Ulyanov","doi":"10.1137/s0040585x97t990605","DOIUrl":"https://doi.org/10.1137/s0040585x97t990605","url":null,"abstract":"","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"87 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77567887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1137/s0040585x97t990599
A. Aparin, G. A. Popov, E. Yarovaya
{"title":"On the Sojourn Time Distribution of a Random Walk at a Multidimensional Lattice Point","authors":"A. Aparin, G. A. Popov, E. Yarovaya","doi":"10.1137/s0040585x97t990599","DOIUrl":"https://doi.org/10.1137/s0040585x97t990599","url":null,"abstract":"","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"54 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88124657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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