THE ADVANCES IN APPLIED PROBABILITY TRUST 由 APPLIED PROBABILITY TRUST 出版了 40 多年，是《应用概率杂志》的配套出版物。它包含应用概率学家感兴趣的数学和科学论文，重点是广泛学科的应用，包括生物科学、运筹学、电信、计算机科学、工程、流行病学、金融数学、物理和社会科学以及任何使用随机建模的字段。提交给 APPLIED PROBABILITY 代表的提交内容可能会根据主编的判断出现在 JOURNAL OF APPLIED PROBABILITY 或 ADVANCES IN APPLIED PROBABILITY 中。通常，较短的论文出现在 JOURNAL 中，较长的论文出现在 ADVANCES 中。

Advances in Applied Probability, published by the Applied Probability Trust for over 40 years, serves as a companion publication to the Journal of Applied Probability. It features mathematical and scientific papers of interest to applied probabilists, focusing on a wide range of applications across disciplines including biological sciences, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, physics, and social sciences, as well as any field that utilizes stochastic modeling. Submissions to the Journal of Applied Probability may appear in either the Journal of Applied Probability or Advances in Applied Probability, at the discretion of the editor-in-chief. Typically, shorter papers are published in the Journal, while longer papers are published in Advances.

《Advances in Applied Probability》是由应用概率信托（Applied Probability Trust）出版的期刊，已有40多年的历史，是《应用概率杂志》（Journal of Applied Probability）的配套出版物。该期刊包含应用概率学家感兴趣的数学和科学论文，重点关注广泛学科的应用，包括生物科学、运筹学、电信、计算机科学、工程、流行病学、金融数学、物理和社会科学等领域，以及任何使用随机建模的领域。提交给《应用概率杂志》的稿件，可能会根据主编的判断，出现在《应用概率杂志》或《Advances in Applied Probability》中。通常，较短的论文会发表在《应用概率杂志》中，而较长的论文则会发表在《Advances in Applied Probability》中。

Advances in Applied Probability

Abstract This paper obtains logarithmic asymptotics of moderate deviations of the stochastic process of the number of customers in a many-server queue with generally distributed inter-arrival and service times under a heavy-traffic scaling akin to the Halfin–Whitt regime. The deviation function is expressed in terms of the solution to a Fredholm equation of the second kind. A key element of the proof is the large-deviation principle in the scaling of moderate deviations for the sequential empirical process. The techniques of large-deviation convergence and idempotent processes are used extensively.

Anatolii Puhalskii

Moderate deviations of many-server queues via idempotent processes

基于幂等过程的多服务队列的中等偏差

Abstract We provide explicit small-time formulae for the at-the-money implied volatility, skew, and curvature in a large class of models, including rough volatility models and their multi-factor versions. Our general setup encompasses both European options on a stock and VIX options, thereby providing new insights on their joint calibration. The tools used are essentially based on Malliavin calculus for Gaussian processes. We develop a detailed theoretical and numerical analysis of the two-factor rough Bergomi model and provide insights on the interplay between the different parameters for joint SPX–VIX smile calibration.

Antoine Jacquier

Aitor Muguruza

Alexandre Pannier

Rough multi-factor volatility for SPX and VIX options

SPX和VIX期权的粗糙多因素波动率

Abstract We introduce a modification of the generalized Pólya urn model containing two urns, and we study the number of balls $B_j(n)$ of a given color $j\in\{1,\ldots,J\}$ added to the urns after n draws, where $J\in\mathbb{N}$ . We provide sufficient conditions under which the random variables $(B_j(n))_{n\in\mathbb{N}}$ , properly normalized and centered, converge weakly to a limiting random variable. The result reveals a similar trichotomy as in the classical case with one urn, one of the main differences being that in the scaling we encounter 1-periodic continuous functions. Another difference in our results compared to the classical urn models is that the phase transition of the second-order behavior occurs at $\sqrt{\rho}$ and not at $\rho/2$ , where $\rho$ is the dominant eigenvalue of the mean replacement matrix.

Konrad Kolesko

Ecaterina Sava-Huss

Gaussian fluctuations for the two-urn model

两缸模型的高斯波动

Abstract We analyze the process M ( t ) representing the maximum of the one-dimensional telegraph process X ( t ) with exponentially distributed upward random times and generally distributed downward random times. The evolution of M ( t ) is governed by an alternating renewal of two phases: a rising phase R and a constant phase C . During a rising phase, X ( t ) moves upward, whereas, during a constant phase, it moves upward and downward, continuing to move until it attains the maximal level previously reached. Under some choices of the distribution of the downward times, we are able to determine the distribution of C , which allows us to obtain some bounds for the survival function of M ( t ). In the particular case of exponential downward random times, we derive an explicit expression for the survival function of M ( t ). Finally, the moments of the first passage time $\Theta_w$ of the process X ( t ) through a fixed boundary $w&gt;0$ are analyzed.

Barbara Martinucci

Paola Paraggio

Shelemyahu Zacks

Some results on the supremum and on the first passage time of the generalized telegraph process

广义电报过程的上确界与首次通过时间的若干结果

Abstract We derive some key extremal features for stationary k th-order Markov chains that can be used to understand how the process moves between an extreme state and the body of the process. The chains are studied given that there is an exceedance of a threshold, as the threshold tends to the upper endpoint of the distribution. Unlike previous studies with $k&gt;1$ , we consider processes where standard limit theory describes each extreme event as a single observation without any information about the transition to and from the body of the distribution. Our work uses different asymptotic theory which results in non-degenerate limit laws for such processes. We study the extremal properties of the initial distribution and the transition probability kernel of the Markov chain under weak assumptions for broad classes of extremal dependence structures that cover both asymptotically dependent and asymptotically independent Markov chains. For chains with $k&gt;1$ , the transition of the chain away from the exceedance involves novel functions of the k previous states, in comparison to just the single value, when $k=1$ . This leads to an increase in the complexity of determining the form of this class of functions, their properties, and the method of their derivation in applications. We find that it is possible to derive an affine normalization, dependent on the threshold excess, such that non-degenerate limiting behaviour of the process, in the neighbourhood of the threshold excess, is assured for all lags. We find that these normalization functions have an attractive structure that has parallels to the Yule–Walker equations. Furthermore, the limiting process is always linear in the innovations. We illustrate the results with the study of k th-order stationary Markov chains with exponential margins based on widely studied families of copula dependence structures.

Ioannis Papastathopoulos

Adrian Casey

Jonathan A. Tawn

Hidden tail chains and recurrence equations for dependence parameters associated with extremes of stationary higher-order Markov chains

静止高阶马尔可夫链极端依赖参数的隐藏尾链与递推方程

Abstract In Chung–Lu random graphs, a classic model for real-world networks, each vertex is equipped with a weight drawn from a power-law distribution, and two vertices form an edge independently with probability proportional to the product of their weights. Chung–Lu graphs have average distance $O(\log\log n)$ and thus reproduce the small-world phenomenon, a key property of real-world networks. Modern, more realistic variants of this model also equip each vertex with a random position in a specific underlying geometry. The edge probability of two vertices then depends, say, inversely polynomially on their distance. In this paper we study a generic augmented version of Chung–Lu random graphs. We analyze a model where the edge probability of two vertices can depend arbitrarily on their positions, as long as the marginal probability of forming an edge (for two vertices with fixed weights, one fixed position, and one random position) is as in a Chung–Lu random graph. The resulting class contains Chung–Lu random graphs, hyperbolic random graphs, and geometric inhomogeneous random graphs as special cases. Our main result is that every random graph model in this general class has the same average distance as a Chung–Lu random graph, up to a factor of $1+o(1)$ . This shows in particular that specific choices, such as taking the underlying geometry to be Euclidean, do not significantly influence the average distance. The proof also shows that every random graph model in our class has a giant component and polylogarithmic diameter with high probability.

Karl Bringmann

Ralph Keusch

Johannes Lengler

Average distance in a general class of scale-free networks

一类无标度网络中的平均距离

Abstract We solve the non-discounted, finite-horizon optimal stopping problem of a Gauss–Markov bridge by using a time-space transformation approach. The associated optimal stopping boundary is proved to be Lipschitz continuous on any closed interval that excludes the horizon, and it is characterized by the unique solution of an integral equation. A Picard iteration algorithm is discussed and implemented to exemplify the numerical computation and geometry of the optimal stopping boundary for some illustrative cases.

Abel Azze

Bernardo D’Auria

Eduardo García-Portugués

Optimal stopping of Gauss–Markov bridges

高斯-马尔可夫桥的最优停止

Abstract We present a closed-form solution to a discounted optimal stopping zero-sum game in a model based on a generalised geometric Brownian motion with coefficients depending on its running maximum and minimum processes. The optimal stopping times forming a Nash equilibrium are shown to be the first times at which the original process hits certain boundaries depending on the running values of the associated maximum and minimum processes. The proof is based on the reduction of the original game to the equivalent coupled free-boundary problem and the solution of the latter problem by means of the smooth-fit and normal-reflection conditions. We show that the optimal stopping boundaries are partially determined as either unique solutions to the appropriate system of arithmetic equations or unique solutions to the appropriate first-order nonlinear ordinary differential equations. The results obtained are related to the valuation of the perpetual lookback game options with floating strikes in the appropriate diffusion-type extension of the Black–Merton–Scholes model.

Abbreviation	Adv. Appl. Probab.
Journal Impact	0.70
Quartiles(Global)	STATISTICS & PROBABILITY(Q3)

ISSN	0001-8678, 1475-6064
h-index	63

Publication Information	Publisher: Cambridge University Press，Publishing cycle: Quarterly，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 1996，Proportion of original research papers: 100.00%，Self Citation Rate:0.00%， Gold OA Rate: 0.00%
Average review cycle	网友分享经验：较慢,6-12周
Average recruitment ratio	网友分享经验：容易

Advances in Applied Probability

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Moderate deviations of many-server queues via idempotent processes

Rough multi-factor volatility for SPX and VIX options

Gaussian fluctuations for the two-urn model

Some results on the supremum and on the first passage time of the generalized telegraph process

Hidden tail chains and recurrence equations for dependence parameters associated with extremes of stationary higher-order Markov chains

Moderate deviations of many-server queues via idempotent processes

Rough multi-factor volatility for SPX and VIX options

Average distance in a general class of scale-free networks

Optimal stopping of Gauss–Markov bridges

Discounted optimal stopping zero-sum games in diffusion type models with maxima and minima