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Critical branching processes in a sparse random environment 稀疏随机环境下的临界分支过程
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2023-06-11 DOI: 10.15559/23-vmsta231
D. Buraczewski, Congzao Dong, A. Iksanov, A. Marynych
{"title":"Critical branching processes in a sparse random environment","authors":"D. Buraczewski, Congzao Dong, A. Iksanov, A. Marynych","doi":"10.15559/23-vmsta231","DOIUrl":"https://doi.org/10.15559/23-vmsta231","url":null,"abstract":"We introduce a branching process in a sparse random environment as an intermediate model between a Galton–Watson process and a branching process in a random environment. In the critical case we investigate the survival probability and prove Yaglom-type limit theorems, that is, limit theorems for the size of population conditioned on the survival event.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"04 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85943171","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
The Burgers equation driven by a stochastic measure 由随机测量驱动的汉堡方程
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2023-01-01 DOI: 10.15559/23-vmsta224
V. Radchenko
{"title":"The Burgers equation driven by a stochastic measure","authors":"V. Radchenko","doi":"10.15559/23-vmsta224","DOIUrl":"https://doi.org/10.15559/23-vmsta224","url":null,"abstract":"The class of one-dimensional equations driven by a stochastic measure μ is studied. For μ only σ-additivity in probability is assumed. This class of equations includes the Burgers equation and the heat equation. The existence and uniqueness of the solution are proved, and the averaging principle for the equation is studied.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"17 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72633132","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
On some composite Kies families: distributional properties and saturation in Hausdorff sense 一些复合Kies族:分布性质和Hausdorff意义上的饱和度
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2023-01-01 DOI: 10.15559/23-vmsta227
Tsvetelin S. Zaevski, N. Kyurkchiev
{"title":"On some composite Kies families: distributional properties and saturation in Hausdorff sense","authors":"Tsvetelin S. Zaevski, N. Kyurkchiev","doi":"10.15559/23-vmsta227","DOIUrl":"https://doi.org/10.15559/23-vmsta227","url":null,"abstract":"The stochastic literature contains several extensions of the exponential distribution which increase its applicability and flexibility. In the present article, some properties of a new power modified exponential family with an original Kies correction are discussed. This family is defined as a Kies distribution which domain is transformed by another Kies distribution. Its probabilistic properties are investigated and some limitations for the saturation in the Hausdorff sense are derived. Moreover, a formula of a semiclosed form is obtained for this saturation. Also the tail behavior of these distributions is examined considering three different criteria inspired by the financial markets, namely, the VaR, AVaR, and expectile based VaR. Some numerical experiments are provided, too.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"183 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76045668","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
A modified Φ-Sobolev inequality for canonical Lévy processes and its applications 典型lsamvy过程的修正Φ-Sobolev不等式及其应用
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2023-01-01 DOI: 10.15559/23-vmsta220
Noriyoshi Sakuma, R. Suzuki
{"title":"A modified Φ-Sobolev inequality for canonical Lévy processes and its applications","authors":"Noriyoshi Sakuma, R. Suzuki","doi":"10.15559/23-vmsta220","DOIUrl":"https://doi.org/10.15559/23-vmsta220","url":null,"abstract":"A new modified Φ-Sobolev inequality for canonical ${L^{2}}$-Lévy processes, which are hybrid cases of the Brownian motion and pure jump-Lévy processes, is developed. Existing results included only a part of the Brownian motion process and pure jump processes. A generalized version of the Φ-Sobolev inequality for the Poisson and Wiener spaces is derived. Furthermore, the theorem can be applied to obtain concentration inequalities for canonical Lévy processes. In contrast to the measure concentration inequalities for the Brownian motion alone or pure jump Lévy processes alone, the measure concentration inequalities for canonical Lévy processes involve Lambert’s W-function. Examples of inequalities are also presented, such as the supremum of Lévy processes in the case of mixed Brownian motion and Poisson processes.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"1983 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90299840","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
Ruin probabilities as functions of the roots of a polynomial 破产概率作为多项式根的函数
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2023-01-01 DOI: 10.15559/23-vmsta226
David J. Santana, Luis Rincón
{"title":"Ruin probabilities as functions of the roots of a polynomial","authors":"David J. Santana, Luis Rincón","doi":"10.15559/23-vmsta226","DOIUrl":"https://doi.org/10.15559/23-vmsta226","url":null,"abstract":"A new formula for the ultimate ruin probability in the Cramér–Lundberg risk process is provided when the claims are assumed to follow a finite mixture of m Erlang distributions. Using the theory of recurrence sequences, the method proposed here shifts the problem of finding the ruin probability to the study of an associated characteristic polynomial and its roots. The found formula is given by a finite sum of terms, one for each root of the polynomial, and allows for yet another approximation of the ruin probability. No constraints are assumed on the multiplicity of the roots and that is illustrated via a couple of numerical examples.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"37 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76394184","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
On geometric recurrence for time-inhomogeneous autoregression 时间非齐次自回归的几何递归
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2023-01-01 DOI: 10.15559/23-vmsta228
V. Golomoziy
{"title":"On geometric recurrence for time-inhomogeneous autoregression","authors":"V. Golomoziy","doi":"10.15559/23-vmsta228","DOIUrl":"https://doi.org/10.15559/23-vmsta228","url":null,"abstract":"The time-inhomogeneous autoregressive model AR(1) is studied, which is the process of the form Xn+1=αnXn+εn, where αn are constants, and εn are independent random variables. Conditions on αn and distributions of εn are established that guarantee the geometric recurrence of the process. This result is applied to estimate the stability of n-steps transition probabilities for two autoregressive processes X(1) and X(2) assuming that both αn(i), i∈{1,2}, and distributions of εn(i), i∈{1,2}, are close enough.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"44 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79383937","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
2010 Mathematics Subject Classification index 2010年数学学科分类指数
Modern Stochastics-Theory and Applications Pub Date : 2023-01-01 DOI: 10.15559/23-vmsta104mi
{"title":"2010 Mathematics Subject Classification index","authors":"","doi":"10.15559/23-vmsta104mi","DOIUrl":"https://doi.org/10.15559/23-vmsta104mi","url":null,"abstract":"","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136303754","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
BDG inequalities and their applications for model-free continuous price paths with instant enforcement 即时执行无模型连续价格路径的BDG不等式及其应用
Modern Stochastics-Theory and Applications Pub Date : 2023-01-01 DOI: 10.15559/23-vmsta233
Rafał Marcin Łochowski
{"title":"BDG inequalities and their applications for model-free continuous price paths with instant enforcement","authors":"Rafał Marcin Łochowski","doi":"10.15559/23-vmsta233","DOIUrl":"https://doi.org/10.15559/23-vmsta233","url":null,"abstract":"Shafer and Vovk introduce in their book [8] the notion of instant enforcement and instantly blockable properties. However, they do not associate these notions with any outer measure, unlike what Vovk did in the case of sets of “typical” price paths. In this paper an outer measure on the space $[0,+infty )times Omega $ is introduced, which assigns zero value exactly to those sets (properties) of pairs of time t and an elementary event ω which are instantly blockable. Next, for a slightly modified measure, Itô’s isometry and BDG inequalities are proved, and then they are used to define an Itô-type integral. Additionally, few properties are proved for the quadratic variation of model-free continuous martingales, which hold with instant enforcement.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135952829","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
Keywords index 关键字索引
Modern Stochastics-Theory and Applications Pub Date : 2023-01-01 DOI: 10.15559/23-vmsta104ki
{"title":"Keywords index","authors":"","doi":"10.15559/23-vmsta104ki","DOIUrl":"https://doi.org/10.15559/23-vmsta104ki","url":null,"abstract":"","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136301482","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
Variance Gamma (nonlocal) equations 方差伽玛(非局部)方程
Modern Stochastics-Theory and Applications Pub Date : 2023-01-01 DOI: 10.15559/23-vmsta232
Fausto Colantoni
{"title":"Variance Gamma (nonlocal) equations","authors":"Fausto Colantoni","doi":"10.15559/23-vmsta232","DOIUrl":"https://doi.org/10.15559/23-vmsta232","url":null,"abstract":"Some equations are provided for the Variance Gamma process using the definition other than that based on a time-changed Brownian motion. A new nonlocal equation is obtained involving generalized Weyl derivatives, which is true even in the drifted case. The connection to special functions is in focus, and a space equation for the process is studied. In conclusion, the convergence in distribution of a compound Poisson process to the Variance Gamma process is observed.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135700850","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
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