The Annals of Applied Probability

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• REFLECTED AND DOUBLY REFLECTED BSDES WITH JUMPS: A PRIORI ESTIMATES AND COMPARISON AI翻译
  作者：Crepey, Stephane; Matoussi, Anis
  作者单位：Universite Paris Saclay; Le Mans Universite
  摘要：It is now established that under quite general circumstances, including in models with jumps, the existence of a solution to a reflected BSDE is guaranteed under mild conditions, whereas the existence of a solution to a doubly reflected BSDE is essentially equivalent to the so-called Mokobodski condition. As for uniqueness of solutions, this holds under mild integrability conditions. However, for practical purposes, existence and uniqueness are not enough. In order to further develop these res...
• Mafia: A theoretical study of players and coalitions in a partial information environment AI翻译
  作者：Braverman, Mark; Etesami, Omid; Mossel, Elchanan
  作者单位：University of Toronto; University of California System; University of California Berkeley; University of California System; University of California Berkeley
  摘要：In this paper, we study a game called Mafia, in which different players have different types of information, communication and functionality. The players communicate and function in a way that resembles some real-life situations. We consider two types of operations. First, there are operations that follow an open democratic discussion. Second, some subgroups of players who may have different interests make decisions based on their own group interest. A key ingredient here is that the identity ...
• Asymptotic normality of the k-core in random graphs AI翻译
  作者：Janson, Svante; Luczak, Malwina J.
  作者单位：Uppsala University; University of London; London School Economics & Political Science
  摘要：We study the k-core of a random (multi)graph on n vertices with a given degree sequence. In our previous paper [Random Structures Algorithms 30 (2007) 50-62] we used properties of empirical distributions of independent random variables to give a simple proof of the fact that the size of the giant k-core obeys a law of large numbers as n -> infinity. Here we develop the method further and show that the fluctuations around the deterministic limit converge to a Gaussian law above and near the thr...
• Stochastic control problems for systems driven by normal martingales AI翻译
  作者：Buckdahn, Rainer; Ma, Jin; Rainer, Catherine
  作者单位：Universite de Bretagne Occidentale; University of Southern California; Purdue University System; Purdue University
  摘要：In this paper we study a class of stochastic control problems in which the control of the jump size is essential. Such a model is a generalized version for various applied problems ranging from optimal reinsurance selections for general insurance models to queueing theory. The main novel point of such a control problem is that by changing the jump size of the system, one essentially changes the type of the driving martingale. Such a feature does not seem to have been investigated in any existi...
• Intensity process and compensator: A new filtration expansion approach and the Jeulin-Yor theorem AI翻译
  作者：Guo, Xin; Zeng, Yan
  作者单位：University of California System; University of California Berkeley; Bloomberg L.P.
  摘要：Let (X-t)(t >= 0) be a continuous-time, time-homogeneous strong Markov process with possible jumps and let tau be its first hitting time of a Borel subset of the state space. Suppose X is sampled at random times and suppose also that X has not hit the Borel set by time t. What is the intensity process of tau based on this information? This question from credit risk encompasses basic mathematical problems concerning the existence of an intensity process and filtration expansions, as well as som...
• Evolutionarily stable strategies of random games, and the vertices of random polygons AI翻译
  作者：Hart, Sergiu; Rinott, Yosef; Weiss, Benjamin
  作者单位：Hebrew University of Jerusalem; Hebrew University of Jerusalem; Hebrew University of Jerusalem
  摘要：An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative (mutant) strategies. Unlike Nash equilibria, ESS do not always exist in finite games. In this paper we address the question of what happens when the size of the game increases: does an ESS exist for almost every large game? Letting the entries in the n x n game matrix be independently randomly chosen according to a distribution F, we study the number of ESS with support of size 2....
• Computable exponential bounds for screened estimation and simulation AI翻译
  作者：Kontoyiannis, Loannls; Meyn, Sean R.
  作者单位：Athens University of Economics & Business; University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
  摘要：Suppose the expectation E(F(X)) is to be estimated by the empirical averages of the values of F on independent and identically distributed samples (Xi). A sampling rule called the screened estimator is introduced, and its performance is studied. When the mean E(U(X)) of a different function U is known, the estimates are screened, in that we only consider those which correspond to times when the empirical average of the [U(Xi)) is sufficiently close to its known mean. As long as U dominates F a...
• Optimal investment and consumption in a Black-Scholes market with Levy-driven stochastic coefficients AI翻译
  作者：Delong, Lukasz; Klueppelberg, Claudia
  作者单位：Warsaw School of Economics; Technical University of Munich
  摘要：In this paper, we investigate an optimal investment and consumption problem for an investor who trades in a Black-Scholes financial market with stochastic coefficients driven by a non-Gaussian Ornstein-Uhlenbeck process. We assume that an agent makes investment and consumption decisions based on a power utility function. By applying the usual separation method in the variables, we are faced with the problem of solving a nonlinear (semilinear) first-order partial integro-differential equation. ...
• Variance bounding Markov chains AI翻译
  作者：Roberts, Gareth O.; Rosenthal, Jeffrey S.
  作者单位：Lancaster University; University of Toronto
  摘要：We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all L-2 functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Peskun order. We close with some applications to Metropolis-Hastings algorithms.
• One-dimensional stepping stone models, sardine genetics and Brownian local time AI翻译
  作者：Durrett, Richard; Restrepo, Mateo
  作者单位：Cornell University; Cornell University
  摘要：Consider a one-dimensional stepping stone model with colonies of size M and per-generation migration probability v, or a voter model on Z in which interactions occur over a distance of order K. Sample one individual at the origin and one at L. We show that if Mv/L and L/K-2 converge to positive finite limits, then the genealogy of the sample converges to a pair of Brownian motions that coalesce after the local time of their difference exceeds an independent exponentially distributed random var...