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International Journal of Stochastic Analysis最新文献

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Maximizing the Mean Exit Time of a Brownian Motion from an Interval 从一个区间最大化布朗运动的平均退出时间
International Journal of Stochastic Analysis Pub Date : 2011-04-05 DOI: 10.1155/2011/296259
M. Lefebvre
{"title":"Maximizing the Mean Exit Time of a Brownian Motion from an Interval","authors":"M. Lefebvre","doi":"10.1155/2011/296259","DOIUrl":"https://doi.org/10.1155/2011/296259","url":null,"abstract":"Let be a controlled one-dimensional standard Brownian motion starting from . The problem of optimally controlling until for the first time is solved explicitly in a particular case. The maximal value that the instantaneous reward given for survival in can take is determined.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125977890","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
A Stochastic Two Species Competition Model: Nonequilibrium Fluctuation and Stability 一个随机的两物种竞争模型:非平衡波动和稳定性
International Journal of Stochastic Analysis Pub Date : 2011-04-03 DOI: 10.1155/2011/489386
G. Samanta
{"title":"A Stochastic Two Species Competition Model: Nonequilibrium Fluctuation and Stability","authors":"G. Samanta","doi":"10.1155/2011/489386","DOIUrl":"https://doi.org/10.1155/2011/489386","url":null,"abstract":"The object of this paper is to study the stability behaviours of the deterministic and stochastic versions of a two-species symmetric competition model. The logistic parameters of the competitive species are perturbed by colored noises or Ornstein-Uhlenbeck processes due to random environment. The Fokker-Planck equation has been used to obtain probability density functions. Here, we have also discussed the relationship between stability behaviours of this model in a deterministic environment and the corresponding model in a stochastic environment.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114222588","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: 9
A -Weibull Counting Process through a Fractional Differential Operator 分数阶微分算子的-Weibull计数过程
International Journal of Stochastic Analysis Pub Date : 2011-03-31 DOI: 10.1155/2011/797656
K. Muralidharan, S. S. Nair
{"title":"A -Weibull Counting Process through a Fractional Differential Operator","authors":"K. Muralidharan, S. S. Nair","doi":"10.1155/2011/797656","DOIUrl":"https://doi.org/10.1155/2011/797656","url":null,"abstract":"We use the -Weibull distribution and define a new counting process using the fractional order. As a consequence, we introduce a -process with -Weibull interarrival times. Some interesting special cases are also discussed which leads to a Mittag-Leffler form.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130730104","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: 1
First Passage Time Moments of Jump-Diffusions with Markovian Switching 具有马尔可夫切换的跳跃扩散的首次通过时间矩
International Journal of Stochastic Analysis Pub Date : 2011-03-20 DOI: 10.1155/2011/501360
Jun Peng, Zaiming Liu
{"title":"First Passage Time Moments of Jump-Diffusions with Markovian Switching","authors":"Jun Peng, Zaiming Liu","doi":"10.1155/2011/501360","DOIUrl":"https://doi.org/10.1155/2011/501360","url":null,"abstract":"Using an integral equation associated with generalized backward Kolmogorov's equation for the transition probability density function, recurrence relations are derived for the moments of the time of first exit of jump-diffusions with Markovian switching. The results are used to find the expectation of first passage time of some financial models.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122088836","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: 2
Optimal Harvesting When the Exchange Rate Is a Semimartingale 汇率为半鞅时的最优收获
International Journal of Stochastic Analysis Pub Date : 2011-01-26 DOI: 10.1155/2011/942478
E. Offen, E. Lungu
{"title":"Optimal Harvesting When the Exchange Rate Is a Semimartingale","authors":"E. Offen, E. Lungu","doi":"10.1155/2011/942478","DOIUrl":"https://doi.org/10.1155/2011/942478","url":null,"abstract":"We consider harvesting in the Black-Scholes Quanto Market when the exchange rate is being modeled by the process 𝐸𝑡=𝐸0exp{𝑋𝑡}, where 𝑋𝑡 is a semimartingale, and we ask the following question: What harvesting strategy 𝛾∗ and the value function Φ maximize the expected total income of an investment? We formulate a singular stochastic control problem and give sufficient conditions for the existence of an optimal strategy. We found that, if the value function is not too sensitive to changes in the prices of the investments, the problem reduces to that of Lungu and Øksendal. However, the general solution of this problem still remains elusive.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129314221","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
Large Deviations for Stochastic Differential Equations on Associated with the Critical Sobolev Brownian Vector Fields 临界Sobolev布朗向量场随机微分方程的大偏差
International Journal of Stochastic Analysis Pub Date : 2011-01-03 DOI: 10.1155/2011/840908
Qinghua Wang
{"title":"Large Deviations for Stochastic Differential Equations on Associated with the Critical Sobolev Brownian Vector Fields","authors":"Qinghua Wang","doi":"10.1155/2011/840908","DOIUrl":"https://doi.org/10.1155/2011/840908","url":null,"abstract":"We obtain a large deviation principle for the stochastic differential equations on the sphere associated with the critical Sobolev Brownian vector fields.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124276435","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: 1
Diffusion Approximations of the Geometric Markov Renewal Processes and Option Price Formulas 几何马尔可夫更新过程与期权价格公式的扩散逼近
International Journal of Stochastic Analysis Pub Date : 2010-12-19 DOI: 10.1155/2010/347105
A. Swishchuk, M. S. Islam
{"title":"Diffusion Approximations of the Geometric Markov Renewal Processes and Option Price Formulas","authors":"A. Swishchuk, M. S. Islam","doi":"10.1155/2010/347105","DOIUrl":"https://doi.org/10.1155/2010/347105","url":null,"abstract":"We consider the geometric Markov renewal processes as a model for a security market and study this processes in a diffusion approximation scheme. Weak convergence analysis and rates of convergence of ergodic geometric Markov renewal processes in diffusion scheme are presented. We present European call option pricing formulas in the case of ergodic, double-averaged, and merged diffusion geometric Markov renewal processes.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131568559","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: 5
A Markov Regime-Switching Marked Point Process for Short-Rate Analysis with Credit Risk 信用风险下短期利率分析的马尔可夫状态切换标记点过程
International Journal of Stochastic Analysis Pub Date : 2010-12-05 DOI: 10.1155/2010/870516
T. Siu
{"title":"A Markov Regime-Switching Marked Point Process for Short-Rate Analysis with Credit Risk","authors":"T. Siu","doi":"10.1155/2010/870516","DOIUrl":"https://doi.org/10.1155/2010/870516","url":null,"abstract":"We investigate a Markov, regime-switching, marked point process for the short-term\u0000interest rate in a market. The intensity of the marked point process is a\u0000bounded, predictable process and is modulated by two observable factors. One is\u0000an economic factor described by a diffusion process, and another one is described\u0000by a Markov chain. The states of the chain are interpreted as different rating\u0000categories of corporate credit ratings issued by rating agencies. We consider a\u0000general pricing kernel which can explicitly price economic, market, and credit\u0000risks. It is shown that the price of a pure discount bond satisfies a system of\u0000coupled partial differential-integral equations under a risk-adjusted measure.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"2010 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129731823","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
Time Reversal of Volterra Processes Driven Stochastic Differential Equations Volterra过程驱动随机微分方程的时间反转
International Journal of Stochastic Analysis Pub Date : 2010-08-17 DOI: 10.1155/2013/790709
L. Decreusefond
{"title":"Time Reversal of Volterra Processes Driven Stochastic Differential Equations","authors":"L. Decreusefond","doi":"10.1155/2013/790709","DOIUrl":"https://doi.org/10.1155/2013/790709","url":null,"abstract":"We consider stochastic differential equations driven by some Volterra processes. Under time reversal, these equations are transformed into past-dependent stochastic differential equations driven by a standard Brownian motion. We are then in position to derive existence and uniqueness of solutions of the Volterra driven SDE considered at the beginning.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121289973","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
Stochastic Integration in Abstract Spaces 抽象空间中的随机积分
International Journal of Stochastic Analysis Pub Date : 2010-08-16 DOI: 10.1155/2010/217372
J. K. Brooks, J. Koziński
{"title":"Stochastic Integration in Abstract Spaces","authors":"J. K. Brooks, J. Koziński","doi":"10.1155/2010/217372","DOIUrl":"https://doi.org/10.1155/2010/217372","url":null,"abstract":"We establish the existence of a stochastic integral in a nuclear space setting as follows. Let 𝐸, 𝐹, and 𝐺 be nuclear spaces which satisfy the following conditions: the spaces are reflexive, complete, bornological spaces such that their strong duals also satisfy these conditions. Assume that there is a continuous bilinear mapping of 𝐸×𝐹 into 𝐺. If 𝐻 is an integrable, 𝐸-valued predictable process and 𝑋 is an 𝐹-valued square integrable martingale, then there exists a 𝐺-valued process (∫𝐻𝑑𝑋)𝑡 called the stochastic integral. The Lebesgue space of these integrable processes is studied and convergence theorems are given. Extensions to general locally convex spaces are presented.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132257330","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: 2
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