Pub Date : 2023-01-01DOI: 10.37190/0208-4147.00127
Piotr Kokoszka, Tim Kutta, Deepak Singh, None Haonan Wang
{"title":"Limit theorems for a higher order time dependent Markov chain model","authors":"Piotr Kokoszka, Tim Kutta, Deepak Singh, None Haonan Wang","doi":"10.37190/0208-4147.00127","DOIUrl":"https://doi.org/10.37190/0208-4147.00127","url":null,"abstract":"","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"8 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":"135594438","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 : 2023-01-01DOI: 10.37190/0208-4147.00132
Stanisław Cichomski, Adam Osękowski
Let $xi$ be an integrable random variable defined on $(Omega, mathcal{F}, mathbb{P})$. Fix $kin mathbb{Z}_+$ and let ${mathcal{G}_{i}^{j}}_{1le i le n, 1le j le k}$ be a reference family of sub-$sigma$-fields of $mathcal{F}$, such that ${mathcal{G}_{i}^{j}}_{1le i le n}$ is a filtration for each $jin {1,2,dots,k}$. In this article we explain the underlying connection between the analysis of the maximal functions of the corresponding coherent vector and basic combinatorial properties of the uncentered Hardy-Littlewood maximal operator. Following a classical approach of Grafakos, Kinnunen and Montgomery-Smith, we establish an appropriate version of the celebrated Doob's maximal estimate.
{"title":"Doob's estimate for coherent random variables and maximal operators on trees","authors":"Stanisław Cichomski, Adam Osękowski","doi":"10.37190/0208-4147.00132","DOIUrl":"https://doi.org/10.37190/0208-4147.00132","url":null,"abstract":"Let $xi$ be an integrable random variable defined on $(Omega, mathcal{F}, mathbb{P})$. Fix $kin mathbb{Z}_+$ and let ${mathcal{G}_{i}^{j}}_{1le i le n, 1le j le k}$ be a reference family of sub-$sigma$-fields of $mathcal{F}$, such that ${mathcal{G}_{i}^{j}}_{1le i le n}$ is a filtration for each $jin {1,2,dots,k}$. In this article we explain the underlying connection between the analysis of the maximal functions of the corresponding coherent vector and basic combinatorial properties of the uncentered Hardy-Littlewood maximal operator. Following a classical approach of Grafakos, Kinnunen and Montgomery-Smith, we establish an appropriate version of the celebrated Doob's maximal estimate.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"24 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":"135594687","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 : 2023-01-01DOI: 10.37190/0208-4147.00091
Anirban Das, M. Denker, A. Levina, Lucia Tabacu
{"title":"Estimation by Stable Motions and its Applications","authors":"Anirban Das, M. Denker, A. Levina, Lucia Tabacu","doi":"10.37190/0208-4147.00091","DOIUrl":"https://doi.org/10.37190/0208-4147.00091","url":null,"abstract":"","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69996784","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 : 2023-01-01DOI: 10.37190/0208-4147.00106
Netzahualcóyotl Castañeda-Leyva
{"title":"Moment inequalities for nonnegative random variables","authors":"Netzahualcóyotl Castañeda-Leyva","doi":"10.37190/0208-4147.00106","DOIUrl":"https://doi.org/10.37190/0208-4147.00106","url":null,"abstract":"","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"44 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":"135594440","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 : 2023-01-01DOI: 10.37190/0208-4147.00092
Akram Saci, A. Redjil, H. Boutabia, O. Kebiri
{"title":"Fractional Stochastic Differential Equations Driven By G-Brownian Motion with Delays","authors":"Akram Saci, A. Redjil, H. Boutabia, O. Kebiri","doi":"10.37190/0208-4147.00092","DOIUrl":"https://doi.org/10.37190/0208-4147.00092","url":null,"abstract":"","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69996838","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 : 2023-01-01DOI: 10.37190/0208-4147.00118
Tomasz Jakubowski, Paweł Maciocha
We give ground-state representation for the fractional Laplacian with Dirichlet condition on the half-line
{"title":"Ground-state representation for fractional Laplacian on half-line","authors":"Tomasz Jakubowski, Paweł Maciocha","doi":"10.37190/0208-4147.00118","DOIUrl":"https://doi.org/10.37190/0208-4147.00118","url":null,"abstract":"We give ground-state representation for the fractional Laplacian with Dirichlet condition on the half-line","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"24 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":"135594439","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 : 2022-03-01DOI: 10.37190/0208-4147.00084
T. Kaufmann, H. Sambale, Christoph Thale
We consider products of uniform random variables from the Stiefel manifold of orthonormal kframes in R, k ≤ n, and random vectors from the n-dimensional lp -ball B n p with certain pradial distributions, p ∈ [1,∞). The distribution of this product geometrically corresponds to the projection of the p-radial distribution on Bp onto a random k-dimensional subspace. We derive large deviation principles (LDPs) on the space of probability measures on R for sequences of such projections.
{"title":"Large deviations for uniform projections of $p$-radial distributions on $ell_p^n$-balls","authors":"T. Kaufmann, H. Sambale, Christoph Thale","doi":"10.37190/0208-4147.00084","DOIUrl":"https://doi.org/10.37190/0208-4147.00084","url":null,"abstract":"We consider products of uniform random variables from the Stiefel manifold of orthonormal kframes in R, k ≤ n, and random vectors from the n-dimensional lp -ball B n p with certain pradial distributions, p ∈ [1,∞). The distribution of this product geometrically corresponds to the projection of the p-radial distribution on Bp onto a random k-dimensional subspace. We derive large deviation principles (LDPs) on the space of probability measures on R for sequences of such projections.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46341505","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 : 2022-02-17DOI: 10.37190/0208-4147.00066
T. Skalski, P. Graczyk, Bartosz Kołodziejek, Maciej Wilczy'nski
Sorted (cid:96) 1 Penalized Estimator (SLOPE) is a relatively new convex regularization method for fitting high-dimensional regression models. SLOPE allows to reduce the model dimension by shrinking some estimates of the regression coefficients completely to zero or by equating the absolute values of some nonzero estimates of these coefficients. This allows to identify situations where some of true regression coefficients are equal. In this article we will introduce the SLOPE pattern, i.e., the set of relations between the true regression coefficients, which can be identified by SLOPE. We will also present new results on the strong consistency of SLOPE estimators and on the strong consistency of pattern recovery by SLOPE when the design matrix is orthogonal and illustrate advantages of the SLOPE clustering in the context of high frequency signal denoising.
{"title":"Pattern recovery and signal denoising by SLOPE when the design matrix is orthogonal","authors":"T. Skalski, P. Graczyk, Bartosz Kołodziejek, Maciej Wilczy'nski","doi":"10.37190/0208-4147.00066","DOIUrl":"https://doi.org/10.37190/0208-4147.00066","url":null,"abstract":"Sorted (cid:96) 1 Penalized Estimator (SLOPE) is a relatively new convex regularization method for fitting high-dimensional regression models. SLOPE allows to reduce the model dimension by shrinking some estimates of the regression coefficients completely to zero or by equating the absolute values of some nonzero estimates of these coefficients. This allows to identify situations where some of true regression coefficients are equal. In this article we will introduce the SLOPE pattern, i.e., the set of relations between the true regression coefficients, which can be identified by SLOPE. We will also present new results on the strong consistency of SLOPE estimators and on the strong consistency of pattern recovery by SLOPE when the design matrix is orthogonal and illustrate advantages of the SLOPE clustering in the context of high frequency signal denoising.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45967744","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 : 2022-02-10DOI: 10.37190/0208-4147.00067
B. E. Asri, Khalid Oufdil, Nacer Ourkiya
In this paper we deal with the problem of the existence and the uniqueness of a solution for one dimensional reflected backward stochastic differential equations with two strictly separated barriers when the generator is allowing a logarithmic growth (|y|| ln |y||+ |z| √ | ln |z||) in the state variables y and z. The terminal value ξ and the obstacle processes (Lt)0≤t≤T and (Ut)0≤t≤T are L-integrable for a suitable p > 2. The main idea is to use the concept of local solution to construct the global one. As applications, we broaden the class of functions for which mixed zero-sum stochastic differential games admit an optimal strategy and the related double obstacle partial differential equation problem has a unique viscosity solution.
{"title":"One dimensional reflected BSDEs with two barriers under logarithmic growth and applications","authors":"B. E. Asri, Khalid Oufdil, Nacer Ourkiya","doi":"10.37190/0208-4147.00067","DOIUrl":"https://doi.org/10.37190/0208-4147.00067","url":null,"abstract":"In this paper we deal with the problem of the existence and the uniqueness of a solution for one dimensional reflected backward stochastic differential equations with two strictly separated barriers when the generator is allowing a logarithmic growth (|y|| ln |y||+ |z| √ | ln |z||) in the state variables y and z. The terminal value ξ and the obstacle processes (Lt)0≤t≤T and (Ut)0≤t≤T are L-integrable for a suitable p > 2. The main idea is to use the concept of local solution to construct the global one. As applications, we broaden the class of functions for which mixed zero-sum stochastic differential games admit an optimal strategy and the related double obstacle partial differential equation problem has a unique viscosity solution.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43927094","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 : 2022-01-01DOI: 10.37190/0208-4147.00055
Gwo Dong Lin, Chin-Yuan Hu
. The semi-Mittag-Leffler (SML) distribution arises as the marginal of a stationary Markovian process, and is a generalization of the well-known Mittag-Leffler (ML) or positive Linnik distribution. Unlike the ML distribution, which has been well established, few properties of the SML distribution are discussed in the literature. In this paper, we derive some more characterizations of the SML and related distributions. By using stochastic inequalities, we further extend some characterizations, including Pitman and Yor’s (2003) result about the hyperbolic sine distribution.
{"title":"On the Semi-Mittag-Leffler Distributions","authors":"Gwo Dong Lin, Chin-Yuan Hu","doi":"10.37190/0208-4147.00055","DOIUrl":"https://doi.org/10.37190/0208-4147.00055","url":null,"abstract":". The semi-Mittag-Leffler (SML) distribution arises as the marginal of a stationary Markovian process, and is a generalization of the well-known Mittag-Leffler (ML) or positive Linnik distribution. Unlike the ML distribution, which has been well established, few properties of the SML distribution are discussed in the literature. In this paper, we derive some more characterizations of the SML and related distributions. By using stochastic inequalities, we further extend some characterizations, including Pitman and Yor’s (2003) result about the hyperbolic sine distribution.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69996312","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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