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International Journal of Stochastic Analysis最新文献

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Stochastic Temporal Data Upscaling Using the Generalized k-Nearest Neighbor Algorithm 基于广义k-最近邻算法的随机时间数据升级
International Journal of Stochastic Analysis Pub Date : 2018-09-24 DOI: 10.1155/2018/2487947
J. Mashford
{"title":"Stochastic Temporal Data Upscaling Using the Generalized k-Nearest Neighbor Algorithm","authors":"J. Mashford","doi":"10.1155/2018/2487947","DOIUrl":"https://doi.org/10.1155/2018/2487947","url":null,"abstract":"Three methods of temporal data upscaling, which may collectively be called the generalized k-nearest neighbor (GkNN) method, are considered. The accuracy of the GkNN simulation of month by month yield is considered (where the term yield denotes the dependent variable). The notion of an eventually well-distributed time series is introduced and on the basis of this assumption some properties of the average annual yield and its variance for a GkNN simulation are computed. The total yield over a planning period is determined and a general framework for considering the GkNN algorithm based on the notion of stochastically dependent time series is described and it is shown that for a sufficiently large training set the GkNN simulation has the same statistical properties as the training data. An example of the application of the methodology is given in the problem of simulating yield of a rainwater tank given monthly climatic data.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126865707","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
Regime-Switching Temperature Dynamics Model for Weather Derivatives 天气导数的状态切换温度动力学模型
International Journal of Stochastic Analysis Pub Date : 2018-07-10 DOI: 10.1155/2018/8534131
S. Gyamerah, P. Ngare, Dennis Ikpe
{"title":"Regime-Switching Temperature Dynamics Model for Weather Derivatives","authors":"S. Gyamerah, P. Ngare, Dennis Ikpe","doi":"10.1155/2018/8534131","DOIUrl":"https://doi.org/10.1155/2018/8534131","url":null,"abstract":"Weather is a key production factor in agricultural crop production and at the same time the most significant and least controllable source of peril in agriculture. These effects of weather on agricultural crop production have triggered a widespread support for weather derivatives as a means of mitigating the risk associated with climate change on agriculture. However, these products are faced with basis risk as a result of poor design and modelling of the underlying weather variable (temperature). In order to circumvent these problems, a novel time-varying mean-reversion Lévy regime-switching model is used to model the dynamics of the deseasonalized temperature dynamics. Using plots and test statistics, it is observed that the residuals of the deseasonalized temperature data are not normally distributed. To model the nonnormality in the residuals, we propose using the hyperbolic distribution to capture the semiheavy tails and skewness in the empirical distributions of the residuals for the shifted regime. The proposed regime-switching model has a mean-reverting heteroskedastic process in the base regime and a Lévy process in the shifted regime. By using the Expectation-Maximization algorithm, the parameters of the proposed model are estimated. The proposed model is flexible as it modelled the deseasonalized temperature data accurately.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128427597","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
Option Price Decomposition in Spot-Dependent Volatility Models and Some Applications 现货相关波动率模型的期权价格分解及其应用
International Journal of Stochastic Analysis Pub Date : 2017-07-31 DOI: 10.1155/2017/8019498
Raúl Merino, J. Vives
{"title":"Option Price Decomposition in Spot-Dependent Volatility Models and Some Applications","authors":"Raúl Merino, J. Vives","doi":"10.1155/2017/8019498","DOIUrl":"https://doi.org/10.1155/2017/8019498","url":null,"abstract":"We obtain a Hull and White type option price decomposition for a general local volatility model. We apply the obtained formula to CEV model. As an application we give an approximated closed formula for the call option price under a CEV model and an approximated short term implied volatility surface. These approximated formulas are used to estimate model parameters. Numerical comparison is performed for our new method with exact and approximated formulas existing in the literature.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"174 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133859182","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
Semigroup Solution of Path-Dependent Second-Order Parabolic Partial Differential Equations 路径相关二阶抛物型偏微分方程的半群解
International Journal of Stochastic Analysis Pub Date : 2017-02-27 DOI: 10.1155/2017/2876961
Sixian Jin, H. Schellhorn
{"title":"Semigroup Solution of Path-Dependent Second-Order Parabolic Partial Differential Equations","authors":"Sixian Jin, H. Schellhorn","doi":"10.1155/2017/2876961","DOIUrl":"https://doi.org/10.1155/2017/2876961","url":null,"abstract":"We apply a new series representation of martingales, developed by Malliavin calculus, to characterize the solution of the second-order path-dependent partial differential equations (PDEs) of parabolic type. For instance, we show that the generator of the semigroup characterizing the solution of the path-dependent heat equation is equal to one-half times the second-order Malliavin derivative evaluated along the frozen path.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134629866","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
Global Stability of Nonlinear Stochastic SEI Epidemic Model with Fluctuations in Transmission Rate of Disease 具有疾病传播率波动的非线性随机SEI流行病模型的全局稳定性
International Journal of Stochastic Analysis Pub Date : 2017-01-23 DOI: 10.1155/2017/6313620
O. M. Otunuga
{"title":"Global Stability of Nonlinear Stochastic SEI Epidemic Model with Fluctuations in Transmission Rate of Disease","authors":"O. M. Otunuga","doi":"10.1155/2017/6313620","DOIUrl":"https://doi.org/10.1155/2017/6313620","url":null,"abstract":"We derive and analyze the dynamic of a stochastic SEI epidemic model for disease spread. Fluctuations in the transmission rate of the disease bring about stochasticity in model. We discuss the asymptotic stability of the infection-free equilibrium by first deriving the closed form deterministic ( ) and stochastic ( ) basic reproductive number. Contrary to some author’s remark that different diffusion rates have no effect on the stability of the disease-free equilibrium, we showed that even if no epidemic invasion occurs with respect to the deterministic version of the SEI model (i.e., ), epidemic can still grow initially (if ) because of the presence of noise in the stochastic version of the model. That is, diffusion rates can have effect on the stability by causing a transient epidemic advance. A threshold criterion for epidemic invasion was derived in the presence of external noise.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128594562","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: 10
Asymptotic Time Averages and Frequency Distributions 渐近时间平均和频率分布
International Journal of Stochastic Analysis Pub Date : 2016-09-05 DOI: 10.1155/2016/2741214
M. El-Taha
{"title":"Asymptotic Time Averages and Frequency Distributions","authors":"M. El-Taha","doi":"10.1155/2016/2741214","DOIUrl":"https://doi.org/10.1155/2016/2741214","url":null,"abstract":"Consider an arbitrary nonnegative deterministic process (in a stochastic setting is a fixed realization, i.e., sample-path of the underlying stochastic process) with state space . Using a sample-path approach, we give necessary and sufficient conditions for the long-run time average of a measurable function of process to be equal to the expectation taken with respect to the same measurable function of its long-run frequency distribution. The results are further extended to allow unrestricted parameter (time) space. Examples are provided to show that our condition is not superfluous and that it is weaker than uniform integrability. The case of discrete-time processes is also considered. The relationship to previously known sufficient conditions, usually given in stochastic settings, will also be discussed. Our approach is applied to regenerative processes and an extension of a well-known result is given. For researchers interested in sample-path analysis, our results will give them the choice to work with the time average of a process or its frequency distribution function and go back and forth between the two under a mild condition.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"405 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126682506","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
A BSDE with Delayed Generator Approach to Pricing under Counterparty Risk and Collateralization 交易对手风险与担保下的时滞发电机定价方法
International Journal of Stochastic Analysis Pub Date : 2016-08-02 DOI: 10.1155/2016/1059303
F. Cordoni, L. Persio
{"title":"A BSDE with Delayed Generator Approach to Pricing under Counterparty Risk and Collateralization","authors":"F. Cordoni, L. Persio","doi":"10.1155/2016/1059303","DOIUrl":"https://doi.org/10.1155/2016/1059303","url":null,"abstract":"We consider a nonlinear pricing problem that takes into account credit risk and funding issues. The aforementioned problem is formulated as a stochastic forward-backward system with delay, both in the forward and in the backward component, whose solution is characterized in terms of viscosity solution to a suitable type of path-dependent PDE.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132370696","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
Optimal Bounds for the Variance of Self-Intersection Local Times 自交局部时间方差的最优界
International Journal of Stochastic Analysis Pub Date : 2016-07-20 DOI: 10.1155/2016/5370627
G. Deligiannidis, S. Utev
{"title":"Optimal Bounds for the Variance of Self-Intersection Local Times","authors":"G. Deligiannidis, S. Utev","doi":"10.1155/2016/5370627","DOIUrl":"https://doi.org/10.1155/2016/5370627","url":null,"abstract":"For a -valued random walk , let be its local time at the site . For , define the -fold self-intersection local time as . Also let be the corresponding quantities for the simple random walk in . Without imposing any moment conditions, we show that the variance of the self-intersection local time of any genuinely -dimensional random walk is bounded above by the corresponding quantity for the simple symmetric random walk; that is, . In particular, for any genuinely -dimensional random walk, with , we have . On the other hand, in dimensions we show that if the behaviour resembles that of simple random walk, in the sense that , then the increments of the random walk must have zero mean and finite second moment.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115678560","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
Analysis of a Priority Queue with Phase-Type Service and Failures 具有阶段型服务和故障的优先队列分析
International Journal of Stochastic Analysis Pub Date : 2016-07-17 DOI: 10.1155/2016/9152701
A. Dudin, S. Dudin
{"title":"Analysis of a Priority Queue with Phase-Type Service and Failures","authors":"A. Dudin, S. Dudin","doi":"10.1155/2016/9152701","DOIUrl":"https://doi.org/10.1155/2016/9152701","url":null,"abstract":"We consider a single server queue with two types of customers. We propose a discipline of flexible priority in access that combines the features of randomization and the threshold type control. We introduce a new class of distributions, phase-type with failures () distribution, that generalizes the well-known phase-type () distribution to the case when failures can occur during service of a customer. The arrival flow is described by the marked Markovian arrival process. The service time distribution is of type with the parameters depending on the type of a customer. Customers of both types can be impatient. Behavior of the system is described by the multidimensional Markov chain. Problem of existence and computation of the stationary distribution of this Markov chain is discussed in brief as well as the problem of computation of the key performance measures of the system. Numerical examples are presented that give some insight into behavior of the system performance measures under different values of the parameters defining the strategy of customers access to service.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"12 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116672987","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: 11
Multiserver Queue with Guard Channel for Priority and Retrial Customers 具有保护通道的多服务器队列用于优先级和重审客户
International Journal of Stochastic Analysis Pub Date : 2016-03-03 DOI: 10.1155/2016/7168359
Kazuki Kajiwara, Tuan Phung-Duc
{"title":"Multiserver Queue with Guard Channel for Priority and Retrial Customers","authors":"Kazuki Kajiwara, Tuan Phung-Duc","doi":"10.1155/2016/7168359","DOIUrl":"https://doi.org/10.1155/2016/7168359","url":null,"abstract":"This paper considers a retrial queueing model where a group of guard channels is reserved for priority and retrial customers. Priority and normal customers arrive at the system according to two distinct Poisson processes. Priority customers are accepted if there is an idle channel upon arrival while normal customers are accepted if and only if the number of idle channels is larger than the number of guard channels. Blocked customers (priority or normal) join a virtual orbit and repeat their attempts in a later time. Customers from the orbit (retrial customers) are accepted if there is an idle channel available upon arrival. We formulate the queueing system using a level dependent quasi-birth-and-death (QBD) process. We obtain a Taylor series expansion for the nonzero elements of the rate matrices of the level dependent QBD process. Using the expansion results, we obtain an asymptotic upper bound for the joint stationary distribution of the number of busy channels and that of customers in the orbit. Furthermore, we develop an efficient numerical algorithm to calculate the joint stationary distribution.","PeriodicalId":196477,"journal":{"name":"International Journal of Stochastic Analysis","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125749188","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: 4
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