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Large deviations for multi-dimensional reflected fractional Brownian motion 多维反射分数布朗运动的大偏差
Stochastics and Stochastic Reports Pub Date : 2003-08-01 DOI: 10.1080/1045112031000155650
K. Majewski
{"title":"Large deviations for multi-dimensional reflected fractional Brownian motion","authors":"K. Majewski","doi":"10.1080/1045112031000155650","DOIUrl":"https://doi.org/10.1080/1045112031000155650","url":null,"abstract":"By proving the continuity of multi-dimensional Skorokhod maps in a quasi-linearly discounted uniform norm on the doubly infinite time interval R, and strengthening know sample path large deviation principles for fractional Brownian motion to this topology, we obtain large deviation principles for the image of multi-dimensional fractional Brownian motions under Skorokhod maps as an immediate consequence of the contraction principle. As an application, we explicitly calculate large deviation decay rates for steady-state tail probabilities of certain queueing systems in multi-dimensional heavy traffic models driven by fractional Brownian motions.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127224821","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
The Robbins–Monro type stochastic differential equations. II. Asymptotic behaviour of solutions 罗宾斯-门罗型随机微分方程。2解的渐近性质
Stochastics and Stochastic Reports Pub Date : 2003-06-01 DOI: 10.1080/1045112031000080239
N. Lazrieva, T. Sharia, T. Toronjadze
{"title":"The Robbins–Monro type stochastic differential equations. II. Asymptotic behaviour of solutions","authors":"N. Lazrieva, T. Sharia, T. Toronjadze","doi":"10.1080/1045112031000080239","DOIUrl":"https://doi.org/10.1080/1045112031000080239","url":null,"abstract":"General results concerning the asymptotic behaviour of the solution of the Robbins–Monro type stochastic differential equations are presented. In particular, the rate of convergence of the solution as is established. Moreover, it is shown that Z admits an asymptotic expansion which enables one to obtain the asymptotic distribution of the randomly normed solution from a martingale limit theorem.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"725 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122999848","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: 13
Stochastic integration with respect to the fractional Brownian motion 关于分数布朗运动的随机积分
Stochastics and Stochastic Reports Pub Date : 2003-06-01 DOI: 10.1080/1045112031000078917
E. Alòs, D. Nualart
{"title":"Stochastic integration with respect to the fractional Brownian motion","authors":"E. Alòs, D. Nualart","doi":"10.1080/1045112031000078917","DOIUrl":"https://doi.org/10.1080/1045112031000078917","url":null,"abstract":"We develop a stochastic calculus for the fractional Brownian motion with Hurst parameter using the techniques of the Malliavin calculus. We establish estimates in L p , maximal inequalities and a continuity criterion for the stochastic integral. Finally, we derive an Itô's formula for integral processes.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134549752","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: 295
Coupling and option price comparisons in a jump-diffusion model 跳跃-扩散模型中的耦合与期权价格比较
Stochastics and Stochastic Reports Pub Date : 2003-06-01 DOI: 10.1080/1045112031000084343
V. Henderson, D. Hobson
{"title":"Coupling and option price comparisons in a jump-diffusion model","authors":"V. Henderson, D. Hobson","doi":"10.1080/1045112031000084343","DOIUrl":"https://doi.org/10.1080/1045112031000084343","url":null,"abstract":"In this paper, we examine the dependence of option prices in a general jump-diffusion model on the choice of martingale pricing measure. Since the model is incomplete, there are many equivalent martingale measures. Each of these measures corresponds to a choice for the market price of diffusion risk and the market price of jump risk. Our main result is to show that for convex payoffs, the option price is increasing in the jump-risk parameter. We apply this result to deduce general inequalities, comparing the prices of contingent claims under various martingale measures, which have been proposed in the literature as candidate pricing measures. Our proofs are based on couplings of stochastic processes. If there is only one possible jump size then we are able to utilize a second coupling to extend our results to include stochastic jump intensities.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122038426","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
SPDEs driven by space-time white noise in high dimensions: absolute continuity of the law and convergence of solutions 高维时空白噪声驱动的SPDEs:定律的绝对连续性和解的收敛性
Stochastics and Stochastic Reports Pub Date : 2003-06-01 DOI: 10.1080/1045112031000080833
Tusheng Zhang, Weian Zheng
{"title":"SPDEs driven by space-time white noise in high dimensions: absolute continuity of the law and convergence of solutions","authors":"Tusheng Zhang, Weian Zheng","doi":"10.1080/1045112031000080833","DOIUrl":"https://doi.org/10.1080/1045112031000080833","url":null,"abstract":"In this paper, we consider stochastic partial differential equations driven by space-time white noise in high dimensions. We prove, under reasonable conditions, that the law of the solution admits a density with respect to Lebesgue measure. The stability of the equation, as the higher order differential operator tends to zero, is also studied in the paper.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"41 24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128494650","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: 14
Solving parabolic Wick-stochastic boundary value problems using a finite element method 用有限元法求解抛物型wick -随机边值问题
Stochastics and Stochastic Reports Pub Date : 2003-01-01 DOI: 10.1080/1045112021000040973
T. G. Theting
{"title":"Solving parabolic Wick-stochastic boundary value problems using a finite element method","authors":"T. G. Theting","doi":"10.1080/1045112021000040973","DOIUrl":"https://doi.org/10.1080/1045112021000040973","url":null,"abstract":"A class of linear parabolic stochastic boundary value problems of Wick-type is studied. The equations are understood in a weak sense on a suitable stochastic distribution space, and existence and uniqueness results are provided. The paper continues to discuss a numerical method for this type of problem, based on a Galerkin type of approximation. Estimates showing linear convergence in time and space are derived, and rate of convergence results for the stochastic dimension are reported.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133460379","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
Maximal inequalities for a continuous semimartingale 连续半鞅的极大不等式
Stochastics and Stochastic Reports Pub Date : 2003-01-01 DOI: 10.1080/1045112021000036554
Litan Yan
{"title":"Maximal inequalities for a continuous semimartingale","authors":"Litan Yan","doi":"10.1080/1045112021000036554","DOIUrl":"https://doi.org/10.1080/1045112021000036554","url":null,"abstract":"Let X =( X t ) t S 0 be a continuous semimartingale given by d X t = f ( t ) w ( X t )d d M ¢ t + f ( t ) σ ( X t )d M t , X 0 =0, where M =( M t , F t ) t S 0 is a continuous local martingale starting at zero with quadratic variation d M ¢ and f ( t ) is a positive, bounded continuous function on [0, X ), and w , σ both are continuous on R and σ ( x )>0 if x p 0. Denote X 𝜏 * =sup 0 h t h 𝜏 | X t | and J t = Z 0 t f ( s ) } ( X s )d d M ¢ s ( t S 0) for a nonnegative continuous function } . If w ( x ) h 0 ( x S 0) and K 1 | x | n σ 2 ( x ) h | w ( x )| h K 2 | x | n σ 2 ( x ) ( x ] R , n >0) with two fixed constants K 2 S K 1 >0, then under suitable conditions for } we show that the maximal inequalities c p , n log 1 n +1 (1+ J 𝜏 ) p h Á X 𝜏 * Á p h C p , n log 1 n +1 (1+ J 𝜏 ) p (0< p < n +1) hold for all stopping times 𝜏 .","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133839613","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: 3
Small time and semiclassical asymptotics for stochastic heat equations driven by Lévy noise 由lsamvy噪声驱动的随机热方程的小时间半经典渐近性
Stochastics and Stochastic Reports Pub Date : 2003-01-01 DOI: 10.1080/1045112021000040964
V. N. Kolokol’tsov, A. Tyukov
{"title":"Small time and semiclassical asymptotics for stochastic heat equations driven by Lévy noise","authors":"V. N. Kolokol’tsov, A. Tyukov","doi":"10.1080/1045112021000040964","DOIUrl":"https://doi.org/10.1080/1045112021000040964","url":null,"abstract":"The paper is devoted to the study of stochastic heat equations driven by Lévy noise. Applying the WKB method, we obtain multiplicative small time and semiclassical asymptotics for the Green functions and for solutions of the Cauchy problem for the heat equation under some natural additional assumptions on their coefficients. The first step in this construction consists in solving the corresponding stochastic Hamilton-Jacobi equations which constitute the \"classical part\" of the semiclassical approximation. In its turn, the corresponding Hamilton-Jacobi equations can be solved via solutions of the corresponding Hamiltonian systems, which gives rise to the method of stochastic characteristics. The relevant theory of stochastic Hamiltonian systems and stochastic Hamilton-Jacobi equations was developed in our previous papers. Here we put the final rung on the ladder: stochastic Hamiltonian systems, stochastic Hamilton-Jacobi equations, stochastic heat equations.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126187136","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: 8
Functional central limit theorems for vicious walkers 恶性步行者的泛函中心极限定理
Stochastics and Stochastic Reports Pub Date : 2002-03-28 DOI: 10.1080/10451120310001633711
M. Katori, H. Tanemura
{"title":"Functional central limit theorems for vicious walkers","authors":"M. Katori, H. Tanemura","doi":"10.1080/10451120310001633711","DOIUrl":"https://doi.org/10.1080/10451120310001633711","url":null,"abstract":"We consider the diffusion scaling limit of the vicious walker model that is a system of nonintersecting random walks. We prove a functional central limit theorem for the model and derive two types of nonintersecting Brownian motions, in which the nonintersecting condition is imposed in a finite time interval for the first type and in an infinite time interval for the second type, respectively. The limit process of the first type is a temporally inhomogeneous diffusion, and that of the second type is a temporally homogeneous diffusion that is identified with a Dyson's model of Brownian motions studied in the random matrix theory. We show that these two types of processes are related to each other by a multi-dimensional generalization of Imhof's relation, whose original form relates the Brownian meander and the three-dimensional Bessel process. We also study the vicious walkers with wall restriction and prove a functional central limit theorem in the diffusion scaling limit.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122236951","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
Risk-sensitive portfolio optimization on infinite time horizon 无限时间范围的风险敏感投资组合优化
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/1045112021000025961
Kazutaka Kuroda, H. Nagai
{"title":"Risk-sensitive portfolio optimization on infinite time horizon","authors":"Kazutaka Kuroda, H. Nagai","doi":"10.1080/1045112021000025961","DOIUrl":"https://doi.org/10.1080/1045112021000025961","url":null,"abstract":"We consider a continuous time portfolio optimization problems on an infinite time horizon for a factor model, recently treated by Bielecki and Pliska [\"Risk-sensitive dynamic asset management\", Appl. Math. Optim. , 39 (1990) 337-360], where the mean returns of individual securities or asset categories are explicitly affected by economic factors. The factors are assumed to be Gaussian processes. We see new features in constructing optimal strategies for risk-sensitive criteria of the portfolio optimization on an infinite time horizon, which are obtained from the solutions of matrix Riccati equations.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124829463","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: 94
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