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A cyclic random motion in R 3 with four directions and finite velocity 在r3中有四个方向和有限速度的循环随机运动
Stochastics and Stochastic Reports Pub Date : 2004-04-01 DOI: 10.1080/1045112042000218829
E. Orsingher, A. Sommella
{"title":"A cyclic random motion in R 3 with four directions and finite velocity","authors":"E. Orsingher, A. Sommella","doi":"10.1080/1045112042000218829","DOIUrl":"https://doi.org/10.1080/1045112042000218829","url":null,"abstract":"In this paper, a cyclic random motion with four directions forming a regular tetrahedron in the Euclidean space R 3 is considered. Changes of direction are governed by a homogenous Poisson process. We obtain the explicit form of the absolutely continuous part of the distribution of the moving particle (X(t), Y(t), Z(t)), in terms of Bessel functions of fourth-order. We prove that the singular part of the distribution is uniformly distributed on the vertices (when no event occurs), on the edges (when one change of direction takes place) and on the faces when two events are recorded. We are also able to obtain (by solving suitable boundary-value problems for the governing equation of the probability generating function) the distribution of (X(t), Y(t), Z(t)) under the condition that the number of Poisson events is fixed. The results of this paper are compared with random motions in the plane and on the line for which the explicit distribution is known.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127278722","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: 12
Invariant Distributions for Singular Stochastic Differential Equations 奇异随机微分方程的不变量分布
Stochastics and Stochastic Reports Pub Date : 2004-04-01 DOI: 10.1080/10451120410001697837
A. Cherny
{"title":"Invariant Distributions for Singular Stochastic Differential Equations","authors":"A. Cherny","doi":"10.1080/10451120410001697837","DOIUrl":"https://doi.org/10.1080/10451120410001697837","url":null,"abstract":"We present necessary and sufficient conditions for the existence of a unique invariant distribution for a one-dimensional stochastic differential equation (SDE) such that this distribution is supported by an interval","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132338959","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
Non-linear degenerate integro-partial differential evolution equations related to geometric Lévy processes and applications to backward stochastic differential equations 与几何lsamvy过程相关的非线性退化积分偏微分演化方程及其在倒向随机微分方程中的应用
Stochastics and Stochastic Reports Pub Date : 2004-04-01 DOI: 10.1080/10451120410001696289
A. Amadori, K. Karlsen, Claudia La Chioma
{"title":"Non-linear degenerate integro-partial differential evolution equations related to geometric Lévy processes and applications to backward stochastic differential equations","authors":"A. Amadori, K. Karlsen, Claudia La Chioma","doi":"10.1080/10451120410001696289","DOIUrl":"https://doi.org/10.1080/10451120410001696289","url":null,"abstract":"We prove a comparison principle for unbounded semicontinuous viscosity sub- and supersolutions of non-linear degenerate parabolic integro-partial differential equations coming from applications in mathematical finance in which geometric Lévy processes act as the underlying stochastic processes for the assets dynamics. As a consequence of the “geometric form” of these processes, the comparison principle holds without assigning spatial boundary data. We present applications of our result to (i) backward stochastic differential equations (BSDEs) and (ii) pricing of European and American derivatives via BSDEs. Regarding (i), we extend previous results on BSDEs in a Lévy setting and the connection to semilinear integro-partial differential equations.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129011828","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: 19
On the approximation of the solutions of stochastic equations with θ-integrals 关于θ-积分随机方程解的近似
Stochastics and Stochastic Reports Pub Date : 2004-04-01 DOI: 10.1080/10451120410001704090
N. Lazakovich, A. Yablonski
{"title":"On the approximation of the solutions of stochastic equations with θ-integrals","authors":"N. Lazakovich, A. Yablonski","doi":"10.1080/10451120410001704090","DOIUrl":"https://doi.org/10.1080/10451120410001704090","url":null,"abstract":"The paper investigates the problem of approximation of stochastic θ-integrals and the solutions of stochastic differential equations. The complete classification of the methods of approximation of stochastic θ-integrals in the convolution algebra is proposed. It is proved that the solutions of stochastic integral equations with θ-integral can be approximated by the solutions of finite-difference equations with averaging.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121342136","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: 6
Measure-valued limits of interacting particle systems with k-nary interactions II. Finite-dimensional limits 具有k-nary相互作用的相互作用粒子系统的测量值极限[j]。有限维空间的限制
Stochastics and Stochastic Reports Pub Date : 2004-02-01 DOI: 10.1080/10451120410001661241
V. Kolokoltsov
{"title":"Measure-valued limits of interacting particle systems with k-nary interactions II. Finite-dimensional limits","authors":"V. Kolokoltsov","doi":"10.1080/10451120410001661241","DOIUrl":"https://doi.org/10.1080/10451120410001661241","url":null,"abstract":"It is shown that Markov chains in describing k-nary interacting particles of d different types approximate (in the continuous state limit) Markov processes on having pseudo-differential generators with symbols p (x,ξ) depending polynomially (degree k) on x. This approximation can be used to prove existence and non-explosion results for the latter processes. Our general scheme of continuous state (or finite-dimensional measure-valued) limits to processes of k-nary interaction yields a unified description of these limits for a large variety of models that are intensively studied in different domains of natural science from interacting particles in statistical mechanics (e.g. coagulation-fragmentation processes) to evolutionary games and multidimensional birth and death processes from biology and social sciences.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117108315","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: 20
On Markov processes with decomposable pseudo-differential generators 具有可分解伪微分发生器的马尔可夫过程
Stochastics and Stochastic Reports Pub Date : 2004-02-01 DOI: 10.1080/10451120410001661250
V. Kolokoltsov
{"title":"On Markov processes with decomposable pseudo-differential generators","authors":"V. Kolokoltsov","doi":"10.1080/10451120410001661250","DOIUrl":"https://doi.org/10.1080/10451120410001661250","url":null,"abstract":"The paper is devoted to the study of Markov processes in finite-dimensional convex cones (especially R d and ) with a decomposable generator, i.e. with a generator of the form where every A n acts as a multiplication operator by a positive, not necessarily bounded, continuous function a n (x) and where every ψ n generates a Lévy process, i.e. a process with i.i.d. increments in R d . The following problems are discussed: (i) existence and uniqueness of Markov or Feller processes with a given generator, (ii) continuous dependence of the process on the coefficients a n and the starting points, (iii) well posedness of the corresponding martingale problem, (iv) generalized solutions to the Dirichlet problem, (v) regularity of boundary points.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"125 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128630950","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: 23
The Wiener Sequential Testing Problem with Finite Horizon 有限视界的Wiener序列检验问题
Stochastics and Stochastic Reports Pub Date : 2004-02-01 DOI: 10.1080/10451120410001663753
P. Gapeev, G. Peskir
{"title":"The Wiener Sequential Testing Problem with Finite Horizon","authors":"P. Gapeev, G. Peskir","doi":"10.1080/10451120410001663753","DOIUrl":"https://doi.org/10.1080/10451120410001663753","url":null,"abstract":"We present a solution of the Bayesian problem of sequential testing of two simple hypotheses about the mean value of an observed Wiener process on the time interval with finite horizon. The method of proof is based on reducing the initial optimal stopping problem to a parabolic free-boundary problem where the continuation region is determined by two continuous curved boundaries. By means of the change-of-variable formula containing the local time of a diffusion process on curves we show that the optimal boundaries can be characterized as a unique solution of the coupled system of two nonlinear integral equations.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"230 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115593248","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: 40
On the Clark-Ocone Theorem for Fractional Brownian Motions with Hurst Parameter bigger than a Half 关于Hurst参数大于1 / 2的分数阶布朗运动的Clark-Ocone定理
Stochastics and Stochastic Reports Pub Date : 2003-12-01 DOI: 10.1080/19451120310001642613
Christian Bender, R. Elliott
{"title":"On the Clark-Ocone Theorem for Fractional Brownian Motions with Hurst Parameter bigger than a Half","authors":"Christian Bender, R. Elliott","doi":"10.1080/19451120310001642613","DOIUrl":"https://doi.org/10.1080/19451120310001642613","url":null,"abstract":"Integration with respect to a fractional Brownian motion with Hurst parameter is related to the inner product: In this paper we provide an example, which shows that multiplication with an indicator function can increase the corresponding norm. We discuss the significance of this result for the quasi-conditional expectation and the fractional Clark-Ocone derivative introduced in Hu and Øksendal [“Fractional White Noise Calculus and Applications to Finance”, IDAQPRT, 6 (2003) 1–32]. Finally, we prove a new version of the fractional Clark-Ocone formula.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122229633","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: 15
Almost sure weak convergence for the circular ensembles of Dyson 几乎可以肯定的是，戴森环形系综的弱收敛性
Stochastics and Stochastic Reports Pub Date : 2003-12-01 DOI: 10.1080/10451120310001641126
G. Blower
{"title":"Almost sure weak convergence for the circular ensembles of Dyson","authors":"G. Blower","doi":"10.1080/10451120310001641126","DOIUrl":"https://doi.org/10.1080/10451120310001641126","url":null,"abstract":"The circular ensembles of Dyson satisfy isoperimetric inequalities and concentration of measure phenomena for large particle numbers analogous to the isoperimetric inequality for surface measure on the sphere in Euclidean space of high dimension. This leads to a geometrical proof of a result of Johansson [Bull. Sci. Math. (2) 112, (1988), 257–304] that the empirical distribution of energy levels under such ensembles converge weakly almost surely to normalized arclength on the unit circle as","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134544994","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
A law of iterated logarithm for increasing self-similar Markov processes 递增自相似马尔可夫过程的迭代对数律
Stochastics and Stochastic Reports Pub Date : 2003-12-01 DOI: 10.1080/10451120310001646014
V. Rivero
{"title":"A law of iterated logarithm for increasing self-similar Markov processes","authors":"V. Rivero","doi":"10.1080/10451120310001646014","DOIUrl":"https://doi.org/10.1080/10451120310001646014","url":null,"abstract":"We consider increasing self-similar Markov processes (X t ,) on ]0,∞[. By using the Lamperti's bijection between self-similar Markov processes and Lévy processes, we determine the functions f for which there exists a constant c∈R+{0} such that lim inf t→∞ X t /f(t)=c with probability 1. The determination of such functions depends on the subordinator ξ associated to X through the distribution of the Lévy exponential functional and the Laplace exponent of ξ. We provide an analogous result for the self-similar Markov process associated to the opposite of a subordinator.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130751631","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: 37
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