{"title":"Memories of Professor Hiroshi Kunita","authors":"Ichiro Shigkeawa","doi":"10.31390/josa.2.3.04","DOIUrl":"https://doi.org/10.31390/josa.2.3.04","url":null,"abstract":"","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133867283","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}
{"title":"On the Works of Hiroshi Kunita in the Sixties","authors":"M. Fukushima","doi":"10.31390/josa.2.3.03","DOIUrl":"https://doi.org/10.31390/josa.2.3.03","url":null,"abstract":"","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128909042","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}
Let T > 0, α > 1 2 . In this work we consider the problem of estimating the drift parameter of the α-Brownian bridge defined as dXt = −α Xt T−tdt + dWt, 0 ≤ t < T , where W is a standard Brownian motion. Assume that the process X is observed equidistantly in time with the step size ∆n := T n+1 , ti = i∆n, i = 0, ..., n. We will propose two approximate maximum likelihood estimators α̂n and ᾱn for the drift parameter α based on the discrete observations Xti , i = 0, ..., n. The consistency of those estimators is studied. Explicit bounds for the Kolmogorov distance in the central limit theorem for the estimators α̂n and ᾱn are obtained.
设T > 0， α > 1。本文研究了α-布朗桥漂移参数的估计问题，定义为dXt = - α Xt T - tdt + dWt, 0≤T < T，其中W为标准布朗运动。假设在时间上等距离观察过程X，其步长∆n:= T n+1, ti = i∆n, i = 0，…基于离散观测值Xti, i = 0，…，我们将对漂移参数α提出两个近似的极大似然估计量α n和α n。研究了这些估计量的相合性。给出了估计量α n和δ n的中心极限定理中Kolmogorov距离的显式界。
{"title":"Berry-Esseen Bounds for Approximate Maximum Likelihood Estimators in the α-Brownian Bridge","authors":"Khalifa Es-Sebaiy, Jabrane Moustaaid, I. Ouassou","doi":"10.31390/josa.2.2.08","DOIUrl":"https://doi.org/10.31390/josa.2.2.08","url":null,"abstract":"Let T > 0, α > 1 2 . In this work we consider the problem of estimating the drift parameter of the α-Brownian bridge defined as dXt = −α Xt T−tdt + dWt, 0 ≤ t < T , where W is a standard Brownian motion. Assume that the process X is observed equidistantly in time with the step size ∆n := T n+1 , ti = i∆n, i = 0, ..., n. We will propose two approximate maximum likelihood estimators α̂n and ᾱn for the drift parameter α based on the discrete observations Xti , i = 0, ..., n. The consistency of those estimators is studied. Explicit bounds for the Kolmogorov distance in the central limit theorem for the estimators α̂n and ᾱn are obtained.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"1998 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123551603","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}
Andressa Gomes, A. Ohashi, F. Russo, Alan Teixeira
Calculus via regularizations and rough paths are two methods to approach stochastic integration and calculus close to pathwise calculus. The origin of rough paths theory is purely deterministic, calculus via regularization is based on deterministic techniques but there is still a probability in the background. The goal of this paper is to establish a connection between stochastically controlled-type processes, a concept reminiscent from rough paths theory, and the so-called weak Dirichlet processes. As a by-product, we present the connection between rough and Stratonovich integrals for cadlag weak Dirichlet processes integrands and continuous semimartingales integrators.
{"title":"Rough Paths and Regularization","authors":"Andressa Gomes, A. Ohashi, F. Russo, Alan Teixeira","doi":"10.31390/JOSA.2.4.01","DOIUrl":"https://doi.org/10.31390/JOSA.2.4.01","url":null,"abstract":"Calculus via regularizations and rough paths are two methods to approach stochastic integration and calculus close to pathwise calculus. The origin of rough paths theory is purely deterministic, calculus via regularization is based on deterministic techniques but there is still a probability in the background. The goal of this paper is to establish a connection between stochastically controlled-type processes, a concept reminiscent from rough paths theory, and the so-called weak Dirichlet processes. As a by-product, we present the connection between rough and Stratonovich integrals for cadlag weak Dirichlet processes integrands and continuous semimartingales integrators.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117269371","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}
In this paper, we construct an anticipating stochastic integral by linearly decompose a class of non Ft-measurable random variables. The result is applied to the derivation of the Itô formula.
本文通过线性分解一类非ft可测随机变量，构造了一个预测随机积分。所得结果应用于Itô公式的推导。
{"title":"Linear Decomposition and Anticipating Integral for Certain Random Variables","authors":"ching-tang wu, J. Yen","doi":"10.31390/JOSA.2.1.06","DOIUrl":"https://doi.org/10.31390/JOSA.2.1.06","url":null,"abstract":"In this paper, we construct an anticipating stochastic integral by linearly decompose a class of non Ft-measurable random variables. The result is applied to the derivation of the Itô formula.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121919408","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}
. To extend several known centered Gaussian processes, we intro- duce a new centered mixed self-similar Gaussian process called the mixed generalized fractional Brownian motion, which could serve as a good model for a larger class of natural phenomena. This process generalizes both the well-known mixed fractional Brownian motion introduced by Cheridito [7] and the generalized fractional Brownian motion introduced by Zili [29]. We study its main stochastic properties, its non-Markovian and non-stationarity characteristics and the conditions under which it is not a semimartingale. We prove the long-range dependence properties of this process.
{"title":"Mixed Generalized Fractional Brownian Motion","authors":"E. Mliki, S. Alajmi","doi":"10.31390/JOSA.2.2.02","DOIUrl":"https://doi.org/10.31390/JOSA.2.2.02","url":null,"abstract":". To extend several known centered Gaussian processes, we intro- duce a new centered mixed self-similar Gaussian process called the mixed generalized fractional Brownian motion, which could serve as a good model for a larger class of natural phenomena. This process generalizes both the well-known mixed fractional Brownian motion introduced by Cheridito [7] and the generalized fractional Brownian motion introduced by Zili [29]. We study its main stochastic properties, its non-Markovian and non-stationarity characteristics and the conditions under which it is not a semimartingale. We prove the long-range dependence properties of this process.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126375601","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}
We construct relativistic quantumMarkov semigroups from covariant completely positive maps. We proceed by generalizing a step in Stinespring’s dilation to a general system of imprimitivity and basing it on Poincarè group. The resulting noise channels are relativistically consistent and the method is applicable to any fundamental particle, though we demonstrate it for the case of light-like particles. The Krauss decomposition of the relativistically consistent completely positive identity preserving maps (our set up is in Heisenberg picture) enables us to construct the covariant quantum Markov semigroups that are uniformly continuous. We induce representations from the little groups to ensure the quantum Markov semigroups that are ergodic due to transitive systems imprimitivity.
{"title":"Covariant Ergodic Quantum Markov Semigroups via Systems of Imprimitivity","authors":"R. Balu","doi":"10.31390/josa.2.4.07","DOIUrl":"https://doi.org/10.31390/josa.2.4.07","url":null,"abstract":"We construct relativistic quantumMarkov semigroups from covariant completely positive maps. We proceed by generalizing a step in Stinespring’s dilation to a general system of imprimitivity and basing it on Poincarè group. The resulting noise channels are relativistically consistent and the method is applicable to any fundamental particle, though we demonstrate it for the case of light-like particles. The Krauss decomposition of the relativistically consistent completely positive identity preserving maps (our set up is in Heisenberg picture) enables us to construct the covariant quantum Markov semigroups that are uniformly continuous. We induce representations from the little groups to ensure the quantum Markov semigroups that are ergodic due to transitive systems imprimitivity.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"429 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114254071","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}
. We analyze the limit behavior of the Wishart matrix W n,d = X n,d X Tn,d constructed from an n × d random matrix X n,d whose entries are given by the increments of the Hermite process. These entries are correlated on the same row, independent from one row to another and their probability distribution is di ff erent on di ff erent rows. We prove that the Wishart matrix converges in law, as d → ∞ , to a diagonal random matrix whose diagonal elements are random variables in the second Wiener chaos. We also estimate the Wasserstein distance associated to this convergence.
． 本文分析了由n × d随机矩阵X n,d构造的Wishart矩阵W n,d = X n,d X Tn,d的极限行为，该随机矩阵X n,d的项由Hermite过程的增量给出。这些项在同一行上是相关的，从一行到另一行是独立的，它们的概率分布在不同的行上是不同的。在第二次Wiener混沌中，我们证明了Wishart矩阵在d→∞时收敛于一个对角元为随机变量的对角随机矩阵。我们还估计了与此收敛相关的Wasserstein距离。
{"title":"Noncentral Limit Theorem for Large Wishart Matrices with Hermite Entries","authors":"Charles-Philippe Diez, C. Tudor","doi":"10.31390/JOSA.2.1.02","DOIUrl":"https://doi.org/10.31390/JOSA.2.1.02","url":null,"abstract":". We analyze the limit behavior of the Wishart matrix W n,d = X n,d X Tn,d constructed from an n × d random matrix X n,d whose entries are given by the increments of the Hermite process. These entries are correlated on the same row, independent from one row to another and their probability distribution is di ff erent on di ff erent rows. We prove that the Wishart matrix converges in law, as d → ∞ , to a diagonal random matrix whose diagonal elements are random variables in the second Wiener chaos. We also estimate the Wasserstein distance associated to this convergence.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129206508","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}
In this paper we introduce a new class of Gaussian singular integrals, the general alternative Gaussian singular integrals and study the boundedness of them in Lp( d), 1 < p < 1 and its weak (1, 1) boundedness with respect to the Gaussian measure following [7] and [1], respectively.
本文引入了一类新的高斯奇异积分，即一般可选高斯奇异积分，并分别研究了它们在Lp(d)， 1 < p < 1及其弱(1,1)有界性下相对于[7]和[1]的高斯测度的有界性。
{"title":"The Boundedness of General Alternative Singular Integrals with Respect to the Gaussian Measure","authors":"Eduardo Navas, E. Pineda, W. Urbina","doi":"10.31390/JOSA.1.4.14","DOIUrl":"https://doi.org/10.31390/JOSA.1.4.14","url":null,"abstract":"In this paper we introduce a new class of Gaussian singular integrals, the general alternative Gaussian singular integrals and study the boundedness of them in Lp( d), 1 < p < 1 and its weak (1, 1) boundedness with respect to the Gaussian measure following [7] and [1], respectively.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"31 4-5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132630374","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}
We obtain error estimates for strong approximations of a diffusion with a diffusion matrix $sigma$ and a drift b by the discrete time process defined recursively X_N((n+1)/N) = X_N(n/N)+N^{1/2}sigma(X_N(n/N))xi(n+1)+N^{-1}b(XN(n/N)); where xi(n); ngeq 1 are i.i.d. random vectors, and apply this in order to approximate the fair price of a game option with a diffusion asset price evolution by values of Dynkin's games with payoffs based on the above discrete time processes. This provides an effective tool for computations of fair prices of game options with path dependent payoffs in a multi asset market with diffusion evolution.
我们通过递归定义的离散时间过程X＿N((n+1)/ n) = X＿N(n/ n)+ n ^1/2sigma (X＿N(n/ n)) {}xi (n+1)+ n ^(XN(n/ n))，得到具有扩散矩阵$sigma$和漂移b的扩散的强逼近的误差估计;其中{}xi (n);n geq 1是i.i.d随机向量，并将其应用于通过基于上述离散时间过程的Dynkin游戏的收益值来近似具有扩散资产价格演变的游戏选项的公平价格。这为具有扩散演化的多资产市场中具有路径依赖收益的博弈期权的公平价格计算提供了一个有效的工具。
{"title":"Error Estimates for Discrete Approximations of Game Options with Multivariate Diffusion Asset Prices","authors":"Y. Kifer","doi":"10.31390/josa.2.3.08","DOIUrl":"https://doi.org/10.31390/josa.2.3.08","url":null,"abstract":"We obtain error estimates for strong approximations of a diffusion with a diffusion matrix $sigma$ and a drift b by the discrete time process defined recursively X_N((n+1)/N) = X_N(n/N)+N^{1/2}sigma(X_N(n/N))xi(n+1)+N^{-1}b(XN(n/N)); where xi(n); ngeq 1 are i.i.d. random vectors, and apply this in order to approximate the fair price of a game option with a diffusion asset price evolution by values of Dynkin's games with payoffs based on the above discrete time processes. This provides an effective tool for computations of fair prices of game options with path dependent payoffs in a multi asset market with diffusion evolution.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126635692","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}
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