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APR volume 53 issue 2 Cover and Back matter APR第53卷第2期封面和封底
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2021-06-01 DOI: 10.1017/apr.2021.15
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引用次数: 0
Continuous-time locally stationary time series models 连续时间局部平稳时间序列模型
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2021-04-28 DOI: 10.1017/apr.2022.64
Annemarie Bitter, R. Stelzer, Bennet Ströh
{"title":"Continuous-time locally stationary time series models","authors":"Annemarie Bitter, R. Stelzer, Bennet Ströh","doi":"10.1017/apr.2022.64","DOIUrl":"https://doi.org/10.1017/apr.2022.64","url":null,"abstract":"Abstract We adapt the classical definition of locally stationary processes in discrete time (see e.g. Dahlhaus, ‘Locally stationary processes’, in Time Series Analysis: Methods and Applications (2012)) to the continuous-time setting and obtain equivalent representations in the time and frequency domains. From this, a unique time-varying spectral density is derived using the Wigner–Ville spectrum. As an example, we investigate time-varying Lévy-driven state space processes, including the class of time-varying Lévy-driven CARMA processes. First, the connection between these two classes of processes is examined. Considering a sequence of time-varying Lévy-driven state space processes, we then give sufficient conditions on the coefficient functions that ensure local stationarity with respect to the given definition.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45214431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Optimal scaling of MCMC beyond Metropolis 大都市以外MCMC的最优缩放
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2021-04-05 DOI: 10.1017/apr.2022.37
Sanket Agrawal, Dootika Vats, K. Łatuszyński, G. Roberts
{"title":"Optimal scaling of MCMC beyond Metropolis","authors":"Sanket Agrawal, Dootika Vats, K. Łatuszyński, G. Roberts","doi":"10.1017/apr.2022.37","DOIUrl":"https://doi.org/10.1017/apr.2022.37","url":null,"abstract":"Abstract The problem of optimally scaling the proposal distribution in a Markov chain Monte Carlo algorithm is critical to the quality of the generated samples. Much work has gone into obtaining such results for various Metropolis–Hastings (MH) algorithms. Recently, acceptance probabilities other than MH are being employed in problems with intractable target distributions. There are few resources available on tuning the Gaussian proposal distributions for this situation. We obtain optimal scaling results for a general class of acceptance functions, which includes Barker’s and lazy MH. In particular, optimal values for Barker’s algorithm are derived and found to be significantly different from that obtained for the MH algorithm. Our theoretical conclusions are supported by numerical simulations indicating that when the optimal proposal variance is unknown, tuning to the optimal acceptance probability remains an effective strategy.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44359286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Measuring reciprocity in a directed preferential attachment network 定向优先依恋网络中互惠性的测量
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2021-03-12 DOI: 10.1017/apr.2021.52
Tiandong Wang, S. Resnick
{"title":"Measuring reciprocity in a directed preferential attachment network","authors":"Tiandong Wang, S. Resnick","doi":"10.1017/apr.2021.52","DOIUrl":"https://doi.org/10.1017/apr.2021.52","url":null,"abstract":"Abstract Empirical studies (e.g. Jiang et al. (2015) and Mislove et al. (2007)) show that online social networks have not only in- and out-degree distributions with Pareto-like tails, but also a high proportion of reciprocal edges. A classical directed preferential attachment (PA) model generates in- and out-degree distributions with power-law tails, but the theoretical properties of the reciprocity feature in this model have not yet been studied. We derive asymptotic results on the number of reciprocal edges between two fixed nodes, as well as the proportion of reciprocal edges in the entire PA network. We see that with certain choices of parameters, the proportion of reciprocal edges in a directed PA network is close to 0, which differs from the empirical observation. This points out one potential problem of fitting a classical PA model to a given network dataset with high reciprocity, and indicates that alternative models need to be considered.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45618728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Moments of Markovian growth–collapse processes 马尔可夫增长时刻——崩溃过程
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2021-03-08 DOI: 10.1017/apr.2021.63
Nicolas Privault
{"title":"Moments of Markovian growth–collapse processes","authors":"Nicolas Privault","doi":"10.1017/apr.2021.63","DOIUrl":"https://doi.org/10.1017/apr.2021.63","url":null,"abstract":"Abstract We apply general moment identities for Poisson stochastic integrals with random integrands to the computation of the moments of Markovian growth–collapse processes. This extends existing formulas for mean and variance available in the literature to closed-form moment expressions of all orders. In comparison with other methods based on differential equations, our approach yields explicit summations in terms of the time parameter. We also treat the case of the associated embedded chain, and provide recursive codes in Maple and Mathematica for the computation of moments and cumulants of any order with arbitrary cut-off moment sequences and jump size functions.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45561560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Can Coherent Predictions be Contradictory? 连贯的预测会自相矛盾吗?
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2021-03-01 DOI: 10.1017/apr.2020.51
K. Burdzy, Soumik Pal
{"title":"Can Coherent Predictions be Contradictory?","authors":"K. Burdzy, Soumik Pal","doi":"10.1017/apr.2020.51","DOIUrl":"https://doi.org/10.1017/apr.2020.51","url":null,"abstract":"Abstract We prove the sharp bound for the probability that two experts who have access to different information, represented by different $sigma$-fields, will give radically different estimates of the probability of an event. This is relevant when one combines predictions from various experts in a common probability space to obtain an aggregated forecast. The optimizer for the bound is explicitly described. This paper was originally titled ‘Contradictory predictions’.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/apr.2020.51","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45985366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Optimally Stopping at a Given Distance from the Ultimate Supremum of a Spectrally Negative Lévy Process 一个特殊负Lévy过程在距极限上模给定距离处的最优停止
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2021-03-01 DOI: 10.1017/apr.2020.54
Mónica B. Carvajal Pinto, K. van Schaik
{"title":"Optimally Stopping at a Given Distance from the Ultimate Supremum of a Spectrally Negative Lévy Process","authors":"Mónica B. Carvajal Pinto, K. van Schaik","doi":"10.1017/apr.2020.54","DOIUrl":"https://doi.org/10.1017/apr.2020.54","url":null,"abstract":"Abstract We consider the optimal prediction problem of stopping a spectrally negative Lévy process as close as possible to a given distance $b geq 0$ from its ultimate supremum, under a squared-error penalty function. Under some mild conditions, the solution is fully and explicitly characterised in terms of scale functions. We find that the solution has an interesting non-trivial structure: if b is larger than a certain threshold then it is optimal to stop as soon as the difference between the running supremum and the position of the process exceeds a certain level (less than b), while if b is smaller than this threshold then it is optimal to stop immediately (independent of the running supremum and position of the process). We also present some examples.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/apr.2020.54","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46149122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
APR volume 53 issue 1 Cover and Back matter APR第53卷第1期封面和封底
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2021-03-01 DOI: 10.1017/apr.2021.5
{"title":"APR volume 53 issue 1 Cover and Back matter","authors":"","doi":"10.1017/apr.2021.5","DOIUrl":"https://doi.org/10.1017/apr.2021.5","url":null,"abstract":"","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/apr.2021.5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48010482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
APR volume 53 issue 1 Cover and Front matter APR第53卷第1期封面和封面问题
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2021-03-01 DOI: 10.1017/apr.2021.4
{"title":"APR volume 53 issue 1 Cover and Front matter","authors":"","doi":"10.1017/apr.2021.4","DOIUrl":"https://doi.org/10.1017/apr.2021.4","url":null,"abstract":"","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/apr.2021.4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45033288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Discounted Optimal Stopping Problems for Maxima of Geometric Brownian Motions With Switching Payoffs 具有切换收益的几何布朗运动极大值的折现最优停止问题
IF 1.2 4区 数学
Advances in Applied Probability Pub Date : 2021-03-01 DOI: 10.1017/apr.2020.57
P. Gapeev, P. Kort, M. Lavrutich
{"title":"Discounted Optimal Stopping Problems for Maxima of Geometric Brownian Motions With Switching Payoffs","authors":"P. Gapeev, P. Kort, M. Lavrutich","doi":"10.1017/apr.2020.57","DOIUrl":"https://doi.org/10.1017/apr.2020.57","url":null,"abstract":"Abstract We present closed-form solutions to some discounted optimal stopping problems for the running maximum of a geometric Brownian motion with payoffs switching according to the dynamics of a continuous-time Markov chain with two states. The proof is based on the reduction of the original problems to the equivalent free-boundary problems and the solution of the latter problems by means of the smooth-fit and normal-reflection conditions. We show that the optimal stopping boundaries are determined as the maximal solutions of the associated two-dimensional systems of first-order nonlinear ordinary differential equations. The obtained results are related to the valuation of real switching lookback options with fixed and floating sunk costs in the Black–Merton–Scholes model.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/apr.2020.57","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43367227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
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