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Communications on Stochastic Analysis最新文献

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On Being an Academic Side Chick: Tales of Two Adjunct Faculty in the Academy That Trained Them 作为一个学术上的小女孩:两个在培养她们的学院兼职教员的故事
Communications on Stochastic Analysis Pub Date : 2019-09-19 DOI: 10.31390/taboo.18.1.05
LaWanda M. Simpkins, D. Tafari
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引用次数: 1
Taboo 18:1 - Full Issue 禁忌18:1-完整发布
Communications on Stochastic Analysis Pub Date : 2019-09-19 DOI: 10.31390/taboo.18.1.12
Taboo Journal
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引用次数: 0
Stochastic Partial Differential Equation SIS Epidemic Models: Modeling and Analysis 随机偏微分方程SIS流行病模型的建模与分析
Communications on Stochastic Analysis Pub Date : 2019-09-01 DOI: 10.31390/cosa.13.3.08
N. Nguyen, G. Yin
{"title":"Stochastic Partial Differential Equation SIS Epidemic Models: Modeling and Analysis","authors":"N. Nguyen, G. Yin","doi":"10.31390/cosa.13.3.08","DOIUrl":"https://doi.org/10.31390/cosa.13.3.08","url":null,"abstract":"The study on epidemic models plays an important role in mathematical biology and mathematical epidemiology. There has been much effort devoted to epidemic models using ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs). Much study has been carried out and substantial progress has been made. In contrast to the development, this work presents an effort from a different angle, namely, modeling and analysis using stochastic partial differential equations (SPDEs). Specifically, we consider dynamic systems featuring SIS (Susceptible-Infected-Susceptible) epidemic models. Our emphasis is on spatial dependent variations and environmental noise. First, a new epidemic model is proposed. Then existence and uniqueness of solutions of the underlying SPDEs are examined. In addition, stochastic partial differential equation models with Markov switching are examined. Our analysis is based on the use of mild solution. Our hope is that this paper will open up windows for investigation of epidemic models from a new angle.","PeriodicalId":53434,"journal":{"name":"Communications on Stochastic Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41977832","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
Subdifferentials of Value Functions in Nonconvex Dynamic Programming for Nonstationary Stochastic Processes 非平稳随机过程非凸动态规划中值函数的次微分
Communications on Stochastic Analysis Pub Date : 2019-09-01 DOI: 10.31390/COSA.13.3.05
B. Mordukhovich, Nobusumi Sagara
{"title":"Subdifferentials of Value Functions in Nonconvex Dynamic Programming for Nonstationary Stochastic Processes","authors":"B. Mordukhovich, Nobusumi Sagara","doi":"10.31390/COSA.13.3.05","DOIUrl":"https://doi.org/10.31390/COSA.13.3.05","url":null,"abstract":"The main goal of this paper is to apply the machinery of variational analysis and generalized differentiation to study infinite horizon stochastic dynamic programming (DP) with discrete time in the Banach space setting without convexity assumptions. Unlike to standard stochastic DP with stationary Markov processes, we investigate here stochastic DP in $L^p$ spaces to deal with nonstationary stochastic processes, which describe a more flexible learning procedure for the decision-maker. Our main concern is to calculate generalized subgradients of the corresponding value function and to derive necessary conditions for optimality in terms of the stochastic Euler inclusion under appropriate Lipschitzian assumptions. The usage of the subdifferential formula for integral functionals on $L^p$ spaces allows us, in particular, to find verifiable conditions to ensure smoothness of the value function without any convexity and/or interiority assumptions.","PeriodicalId":53434,"journal":{"name":"Communications on Stochastic Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44032946","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
Preface 前言
Communications on Stochastic Analysis Pub Date : 2019-09-01 DOI: 10.31390/cosa.13.3.01
H. Kuo, G. Yin
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引用次数: 0
Anticipating Exponential Processes and Stochastic Differential Equations 预测指数过程与随机微分方程
Communications on Stochastic Analysis Pub Date : 2019-09-01 DOI: 10.31390/cosa.13.3.09
C. Hwang, H. Kuo, Kimiaki Saitô
{"title":"Anticipating Exponential Processes and Stochastic Differential Equations","authors":"C. Hwang, H. Kuo, Kimiaki Saitô","doi":"10.31390/cosa.13.3.09","DOIUrl":"https://doi.org/10.31390/cosa.13.3.09","url":null,"abstract":"Exponential processes in the Itô theory of stochastic integration can be viewed in three aspects: multiplicative renormalization, martingales, and stochastic differential equations. In this paper we initiate the study of anticipating exponential processes from these aspects viewpoints. The analogue of martingale property for anticipating stochastic integrals is the near-martingale property. We use examples to illustrate essential ideas and techniques in dealing with anticipating exponential processes and stochastic differential equations. The situation is very different from the Itô theory. 1. Exponential Processes Let B(t), 0 ≤ t ≤ T, be a fixed Brownian motion. Suppose {Ft; 0 ≤ t ≤ T} is the filtration given by this Brownian motion, i.e., Ft = σ{B(s); 0 ≤ s ≤ t} for each t ∈ [0, T ]. Take an {Ft}-adapted stochastic process h(t), 0 ≤ t ≤ T, satisfying the Novikov condition, i.e., E exp [1 2 ∫ T 0 h(t) dt ] <∞. (1.1) The exponential process given by h(t) is defined to be the stochastic process Eh(t) = exp [ ∫ t 0 h(s) dB(s)− 1 2 ∫ t 0 h(s) ds ] , 0 ≤ t ≤ T. (1.2) Note that under the Novikov condition in equation (1.1) we have ∫ T 0 h(t) dt <∞ almost surely so that the Itô integral ∫ t 0 h(s) dB(s) is defined for each t ∈ [0, T ] (see Chapter 5 of the book [7].) The exponential process Eh(t) plays a very important role in the Itô theory of stochastic integration and is widely used in the mathematical finance. It can be viewed and understood in the following three aspects. (1) Multiplicative renormalization: The multiplicative renormalization of a random variable X with nonzero expectation is defined to be the random variable X/EX. Suppose h(t) is a deterministic function in L[0, T ]. Received 2019-10-13; Accepted 2019-10-14; Communicated by guest editor George Yin. 2010 Mathematics Subject Classification. Primary 60H05; Secondary 60H20.","PeriodicalId":53434,"journal":{"name":"Communications on Stochastic Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47222559","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
Hybrid Models and Switching Control with Constraints 混合模型与带约束的切换控制
Communications on Stochastic Analysis Pub Date : 2019-09-01 DOI: 10.31390/cosa.13.3.03
J. Menaldi, M. Robin
{"title":"Hybrid Models and Switching Control with Constraints","authors":"J. Menaldi, M. Robin","doi":"10.31390/cosa.13.3.03","DOIUrl":"https://doi.org/10.31390/cosa.13.3.03","url":null,"abstract":"","PeriodicalId":53434,"journal":{"name":"Communications on Stochastic Analysis","volume":"52 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41248210","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
Non-Nested Monte Carlo Dual Bounds for Multi-Exercisable Options 多可行权期权的非嵌套蒙特卡罗对偶界
Communications on Stochastic Analysis Pub Date : 2019-09-01 DOI: 10.31390/COSA.13.3.02
Xiang Cheng, Z. Jin
{"title":"Non-Nested Monte Carlo Dual Bounds for Multi-Exercisable Options","authors":"Xiang Cheng, Z. Jin","doi":"10.31390/COSA.13.3.02","DOIUrl":"https://doi.org/10.31390/COSA.13.3.02","url":null,"abstract":"We study the optimal marginal value of discrete-time optimal multiple stopping problems and find that it can be formulated as a single optimal stopping optimization as well. Based on this result propose a marginal-value-based lower bound method to achieve a small bound on the iterative error. We further introduce a non-nested upper bound method. The convergence of both methods is analysed. The implementation details and enhancement techniques are discussed as well. Overall, our methods make a good trade-off between the time-efficiency and the tightness in dual bounds.","PeriodicalId":53434,"journal":{"name":"Communications on Stochastic Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48632191","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 Process and its Role in The Development of the Financial Market: Celebrating Professor Chow's Long and Successful Career 随机过程及其在金融市场发展中的作用——纪念周教授漫长而成功的职业生涯
Communications on Stochastic Analysis Pub Date : 2019-09-01 DOI: 10.31390/cosa.13.3.07
Xisuo L. Liu
{"title":"Stochastic Process and its Role in The Development of the Financial Market: Celebrating Professor Chow's Long and Successful Career","authors":"Xisuo L. Liu","doi":"10.31390/cosa.13.3.07","DOIUrl":"https://doi.org/10.31390/cosa.13.3.07","url":null,"abstract":". Stochastic calculus has played an important role in the development of the financial markets in the past 40+ years. The Black-Sholes option pricing model published in 1973 revolutionized the derivatives market. The advances in volatility estimate such as GARCH helped to improve the risk measures and risk management process. Other developments might have contributed to the onsite of the great financial crisis (GFC). In celebrating Professor Chow’s successful career, I would like to share some of the applications of stochastic calculus in the financial engineering, and the role it played in the financial market development.","PeriodicalId":53434,"journal":{"name":"Communications on Stochastic Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46645691","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
Euler-Maruyama Method for Regime Switching Stochastic Differential Equations with Hölder Coefficients 带Hölder系数的状态切换随机微分方程的Euler-Maruyama方法
Communications on Stochastic Analysis Pub Date : 2019-09-01 DOI: 10.31390/cosa.13.3.04
D. Nguyen, S. L. Nguyen
{"title":"Euler-Maruyama Method for Regime Switching Stochastic Differential Equations with Hölder Coefficients","authors":"D. Nguyen, S. L. Nguyen","doi":"10.31390/cosa.13.3.04","DOIUrl":"https://doi.org/10.31390/cosa.13.3.04","url":null,"abstract":"In this paper, we develop Euler-Maruyama scheme for a wideranging class of stochastic differential equations with regime switching under such conditions that allow drift and diffusion coefficients being Hölder continuous. The strong convergence of the numerical method is proved. In addition, the rate of convergence is obtained under similar conditions to the case of usual diffusions. Some numerical examples are provided to illustrate the results.","PeriodicalId":53434,"journal":{"name":"Communications on Stochastic Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48453833","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
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