Pub Date : 2023-07-04DOI: 10.1080/17442508.2023.2229644
Junjun Lang, Jibing Qi, Fei Zhang, Xuejun Wang
In this paper, we investigate the complete f-moment convergence for weighted sums of asymptotically almost negatively associated (AANA, for short) random variables. Our results improve and generalize the corresponding ones of [M.M. Xi, X. Deng, X.J. Wang, and Z.Y. Cheng, convergence and complete convergence for weighted sums of AANA random variables, Commun. Stat. Theory Methods 47(22) (2018), pp. 5604–5613]. As an application of our main results, some results on the complete consistency for the estimator in semiparametric regression models are obtained and a simulation study is provided to assess the finite sample performance of the theoretical results.
{"title":"Complete f-moment convergence for weighted sums of asymptotically almost negatively associated random variables and its application in semiparametric regression models","authors":"Junjun Lang, Jibing Qi, Fei Zhang, Xuejun Wang","doi":"10.1080/17442508.2023.2229644","DOIUrl":"https://doi.org/10.1080/17442508.2023.2229644","url":null,"abstract":"In this paper, we investigate the complete f-moment convergence for weighted sums of asymptotically almost negatively associated (AANA, for short) random variables. Our results improve and generalize the corresponding ones of [M.M. Xi, X. Deng, X.J. Wang, and Z.Y. Cheng, convergence and complete convergence for weighted sums of AANA random variables, Commun. Stat. Theory Methods 47(22) (2018), pp. 5604–5613]. As an application of our main results, some results on the complete consistency for the estimator in semiparametric regression models are obtained and a simulation study is provided to assess the finite sample performance of the theoretical results.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"32 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86112062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-27DOI: 10.1080/17442508.2023.2227752
Maddalena Cavicchioli
We provide a formal definition of an M-state multivariate Markov switching trend, describe its asymptotic distribution, and consider vector autoregressive processes with trends which contain either unit roots or a stationary part. Then, we estimate the coefficients of such models via ordinary least squares , and determine the asymptotic distributions of estimators in terms of functionals on a multivariate Brownian motion.
{"title":"Estimation and asymptotics for vector autoregressive models with unit roots and Markov switching trends","authors":"Maddalena Cavicchioli","doi":"10.1080/17442508.2023.2227752","DOIUrl":"https://doi.org/10.1080/17442508.2023.2227752","url":null,"abstract":"We provide a formal definition of an M-state multivariate Markov switching trend, describe its asymptotic distribution, and consider vector autoregressive processes with trends which contain either unit roots or a stationary part. Then, we estimate the coefficients of such models via ordinary least squares , and determine the asymptotic distributions of estimators in terms of functionals on a multivariate Brownian motion.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"27 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88774409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-29DOI: 10.1080/17442508.2023.2214265
Ana Merkle
In this paper we further develop a notion of causal predictability defined in [A. Merkle, Predictability and Uniqueness of Weak Solutions of Stochastic Differential Equations, Analele Stiintifice ale Universitatii Ovidius Constanta, 2022] as a concept of dependence which is based on Granger's definition of causality. More precisely, in [A. Merkle, Predictability and Uniqueness of Weak Solutions of Stochastic Differential Equations, Analele Stiintifice ale Universitatii Ovidius Constanta, 2022] causal predictability is defined between filtrations, but now we introduce causal predictability between stochastic processes and filtrations. Also, we provide some properties of this new concept. Then we apply the given causality concept to the uniqueness of weak solutions of the stochastic differential equations and in financial mathematics. Granger [Investigating causal relations by econometric models and cross spectral methods, Econometrica. 37 (1969), pp. 424–438] has considered causality concept between time series. In this paper we consider continuous time processes, since continuous time models represent the first step in various applications, such as in finance, econometric practice, neuroscience, epidemiology, climatology, demographic, etc.
{"title":"Causal predictability between stochastic processes and filtrations","authors":"Ana Merkle","doi":"10.1080/17442508.2023.2214265","DOIUrl":"https://doi.org/10.1080/17442508.2023.2214265","url":null,"abstract":"In this paper we further develop a notion of causal predictability defined in [A. Merkle, Predictability and Uniqueness of Weak Solutions of Stochastic Differential Equations, Analele Stiintifice ale Universitatii Ovidius Constanta, 2022] as a concept of dependence which is based on Granger's definition of causality. More precisely, in [A. Merkle, Predictability and Uniqueness of Weak Solutions of Stochastic Differential Equations, Analele Stiintifice ale Universitatii Ovidius Constanta, 2022] causal predictability is defined between filtrations, but now we introduce causal predictability between stochastic processes and filtrations. Also, we provide some properties of this new concept. Then we apply the given causality concept to the uniqueness of weak solutions of the stochastic differential equations and in financial mathematics. Granger [Investigating causal relations by econometric models and cross spectral methods, Econometrica. 37 (1969), pp. 424–438] has considered causality concept between time series. In this paper we consider continuous time processes, since continuous time models represent the first step in various applications, such as in finance, econometric practice, neuroscience, epidemiology, climatology, demographic, etc.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"20 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78324902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-26DOI: 10.1080/17442508.2023.2214266
Kiyoiki Hoshino
Let be a stochastic process with quadratic variation on a probability space and a dense subset of , where is regarded as the infinite interval when . First, we introduce the -module of V-differentiable noncausal processes on Q and V-derivative operator defined on , which enjoys the modularity: for any and . Second, we show that the class forms an -module, where stands for the quadratic variation on Q. As a result, we have the isometry: for any , where stands for the quadratic covariation on Q. Finally, we present universal properties and examples of the stochastic integral I with . This result is essentially used for solving the identification problem from the stochastic Fourier coefficients.
{"title":"On the stochastic differentiability of noncausal processes with respect to the process with quadratic variation","authors":"Kiyoiki Hoshino","doi":"10.1080/17442508.2023.2214266","DOIUrl":"https://doi.org/10.1080/17442508.2023.2214266","url":null,"abstract":"Let be a stochastic process with quadratic variation on a probability space and a dense subset of , where is regarded as the infinite interval when . First, we introduce the -module of V-differentiable noncausal processes on Q and V-derivative operator defined on , which enjoys the modularity: for any and . Second, we show that the class forms an -module, where stands for the quadratic variation on Q. As a result, we have the isometry: for any , where stands for the quadratic covariation on Q. Finally, we present universal properties and examples of the stochastic integral I with . This result is essentially used for solving the identification problem from the stochastic Fourier coefficients.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"90 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84572835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-12DOI: 10.1080/17442508.2023.2211189
A. Dorogovtsev, Mykola B. Vovchanskyi
We show that if drift coefficients of Arratia flows converge in L1(R) or L∞(R) then the 1-point densities associated with these flows converge to the density for the flow with the limit drift. The Arratia flow, a continual system of coalescing Wiener processes that are independent until they meet, was introduced independently as a limit of coalescing random walks in [1], as a system of reflecting Wiener processes in [2] and as a limit of stochastic homeomorphic flows in [3]. If interpreted as a collection of particles started at 0, it is a part of the Brownian web [4]. At the same time, one can construct the Arratia flow with drift using flows of kernels defined in [5] (see [6, §6] for a short explanation) or directly via martingale problems by adapting the method used in [7] to build coalescing stochastic flows with more general dependence between particles (see [8, Chapter 7] for this approach). Following [8, Chapter 7], we consider a modification of the Arratia flow that introduces drift affecting the motion of a particle within the flow. So by an Arratia flow X ≡ {Xa(u, t) | u ∈ R, t ∈ R+} with bounded measurable drift a we understand a collection of random variables such that (1) for every u the process X(u, ·) is an Itô process with diffusion coefficient 1 and drift a; (2) for all t ≥ 0 the mapping Xa(·, t) is monotonically increasing; (3) for any u1, u2 the joint quadratic covariation of the martingale parts of X (u1, ·) and X(u2, ·) equals (t − inf{s | X(u1, s) = X(u2, s)})+, with inf ∅ being equal ∞ by definition. Since the set {Xa(u, t) | u ∈ R} is known to be locally finite for all t > 0 [8, Chapter 7], one defines for any t > 0 the point process {|Xa(A, t)| | A ∈ B(R)}. Studying of such a point process can be performed using point densities (see: [9, 10] for a definition and a representation in terms of Pfaffians in the case of zero drift, respectively; [11, 12] for representations in the case of non-trivial drift; [13, 14] for applications to the study of the above-mentioned point process). In accordance with [9, Appendix B], the following definition is adopted in the present paper: the 1-point density at time t of the point 2020 Mathematics Subject Classification. Primary 60H10; Secondary 60K35, 60G55, 35C10.
{"title":"On 1-point densities for Arratia flows with drift","authors":"A. Dorogovtsev, Mykola B. Vovchanskyi","doi":"10.1080/17442508.2023.2211189","DOIUrl":"https://doi.org/10.1080/17442508.2023.2211189","url":null,"abstract":"We show that if drift coefficients of Arratia flows converge in L1(R) or L∞(R) then the 1-point densities associated with these flows converge to the density for the flow with the limit drift. The Arratia flow, a continual system of coalescing Wiener processes that are independent until they meet, was introduced independently as a limit of coalescing random walks in [1], as a system of reflecting Wiener processes in [2] and as a limit of stochastic homeomorphic flows in [3]. If interpreted as a collection of particles started at 0, it is a part of the Brownian web [4]. At the same time, one can construct the Arratia flow with drift using flows of kernels defined in [5] (see [6, §6] for a short explanation) or directly via martingale problems by adapting the method used in [7] to build coalescing stochastic flows with more general dependence between particles (see [8, Chapter 7] for this approach). Following [8, Chapter 7], we consider a modification of the Arratia flow that introduces drift affecting the motion of a particle within the flow. So by an Arratia flow X ≡ {Xa(u, t) | u ∈ R, t ∈ R+} with bounded measurable drift a we understand a collection of random variables such that (1) for every u the process X(u, ·) is an Itô process with diffusion coefficient 1 and drift a; (2) for all t ≥ 0 the mapping Xa(·, t) is monotonically increasing; (3) for any u1, u2 the joint quadratic covariation of the martingale parts of X (u1, ·) and X(u2, ·) equals (t − inf{s | X(u1, s) = X(u2, s)})+, with inf ∅ being equal ∞ by definition. Since the set {Xa(u, t) | u ∈ R} is known to be locally finite for all t > 0 [8, Chapter 7], one defines for any t > 0 the point process {|Xa(A, t)| | A ∈ B(R)}. Studying of such a point process can be performed using point densities (see: [9, 10] for a definition and a representation in terms of Pfaffians in the case of zero drift, respectively; [11, 12] for representations in the case of non-trivial drift; [13, 14] for applications to the study of the above-mentioned point process). In accordance with [9, Appendix B], the following definition is adopted in the present paper: the 1-point density at time t of the point 2020 Mathematics Subject Classification. Primary 60H10; Secondary 60K35, 60G55, 35C10.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"23 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80658661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-19DOI: 10.1080/17442508.2023.2199124
G. Deugoue, A. Ndongmo Ngana, T. Tachim Medjo
We study in this article a stochastic version of a coupled Allen-Cahn-Navier-Stokes model on a bounded domain of . The model consists of the Navier-Stokes equations for the velocity, coupled with an Allen-Cahn model for the order (phase) parameter. We prove the existence and uniqueness of a local maximal strong solution when the initial data takes values in . Moreover in the two-dimensional case, we prove that our solution is global.
{"title":"Strong solutions for the stochastic Allen-Cahn-Navier-Stokes system","authors":"G. Deugoue, A. Ndongmo Ngana, T. Tachim Medjo","doi":"10.1080/17442508.2023.2199124","DOIUrl":"https://doi.org/10.1080/17442508.2023.2199124","url":null,"abstract":"We study in this article a stochastic version of a coupled Allen-Cahn-Navier-Stokes model on a bounded domain of . The model consists of the Navier-Stokes equations for the velocity, coupled with an Allen-Cahn model for the order (phase) parameter. We prove the existence and uniqueness of a local maximal strong solution when the initial data takes values in . Moreover in the two-dimensional case, we prove that our solution is global.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"54 1","pages":"1294 - 1360"},"PeriodicalIF":1.7,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73897340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-13DOI: 10.1080/17442508.2023.2199125
X. Yang
In this article, we study a class of reflecting stochastic differential equations whose coefficients depend on image measures of solutions under a given initial measure in Wasserstein space . By the penalization method, the image process, which is a diffusion process in , is constrained in a priori given domain . The large deviation principle for this reflecting image process is also established by weak convergence method.
{"title":"Reflecting image-dependent SDEs in Wasserstein space and large deviation principle","authors":"X. Yang","doi":"10.1080/17442508.2023.2199125","DOIUrl":"https://doi.org/10.1080/17442508.2023.2199125","url":null,"abstract":"In this article, we study a class of reflecting stochastic differential equations whose coefficients depend on image measures of solutions under a given initial measure in Wasserstein space . By the penalization method, the image process, which is a diffusion process in , is constrained in a priori given domain . The large deviation principle for this reflecting image process is also established by weak convergence method.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"13 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88848233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.1080/17442508.2022.2084339
Xiaoyan Xu, Mingbo Zhang
In this paper, we deal with a class of reflected anticipated backward stochastic differential equation with convex reflecting boundary conditions. The existence and uniqueness of solution is obtained for equation with Lipschitz and non-Lipschitz generator respectively.
{"title":"Anticipated BSDEs with reflection in convex region","authors":"Xiaoyan Xu, Mingbo Zhang","doi":"10.1080/17442508.2022.2084339","DOIUrl":"https://doi.org/10.1080/17442508.2022.2084339","url":null,"abstract":"In this paper, we deal with a class of reflected anticipated backward stochastic differential equation with convex reflecting boundary conditions. The existence and uniqueness of solution is obtained for equation with Lipschitz and non-Lipschitz generator respectively.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"31 1","pages":"329 - 355"},"PeriodicalIF":1.7,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82963043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.1080/17442508.2022.2084340
N. T. Da, Do Van Loi
In this paper, we prove the existence of a random attractor, the finiteness of its fractal dimension, the random squeezing property, and the existence of a finite number of determining modes for an abstract stochastic 2D hydrodynamical type equations with additive white noise.
{"title":"On the random attractor for stochastic 2D hydrodynamical type equations with additive white noise","authors":"N. T. Da, Do Van Loi","doi":"10.1080/17442508.2022.2084340","DOIUrl":"https://doi.org/10.1080/17442508.2022.2084340","url":null,"abstract":"In this paper, we prove the existence of a random attractor, the finiteness of its fractal dimension, the random squeezing property, and the existence of a finite number of determining modes for an abstract stochastic 2D hydrodynamical type equations with additive white noise.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"5 1","pages":"356 - 376"},"PeriodicalIF":1.7,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89955904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-29DOI: 10.1007/s00780-023-00502-4
S. Bensalem, Nicolás Hernández-Santibánez, Nabil Kazi-Tani
{"title":"A continuous-time model of self-protection","authors":"S. Bensalem, Nicolás Hernández-Santibánez, Nabil Kazi-Tani","doi":"10.1007/s00780-023-00502-4","DOIUrl":"https://doi.org/10.1007/s00780-023-00502-4","url":null,"abstract":"","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"27 1","pages":"503-537"},"PeriodicalIF":1.7,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46186074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：