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作者：Aldous, DJ; Bandyopadhyay, A
作者单位：University of California System; University of California Berkeley; University of Minnesota System; University of Minnesota Twin Cities
摘要：In certain problems in a variety of applied probability settings (from probabilistic analysis of algorithms to statistical physics), the central requirement is to solve a recursive distributional equation of the form X-d = g((xi(i), X-i), i >= 1). Here (xi(i)) and g((.)) are given and the X-i are independent copies of the unknown distribution X. We survey this area, emphasizing examples where the function g((.)) is essentially a maximum or minimum function. We draw attention to the theoretical...
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作者：Bousquet-Mélou, M
作者单位：Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider planar lattice walks that start from (0, 0), remain in the first quadrant i, j >= 0, and are made of three types of steps: North-East, West and South. These walks are known to have remarkable enumerative and probabilistic properties: center dot they are counted by nice numbers [Kreweras, Cahiers du B.U.R.O 6 (1965) 5-105], center dot the generating function of these numbers is algebraic [Gessel, J. Statist. Plann. Inference 14 (1986) 49-58], center dot the stationary distribution o...
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作者：Becherer, D; Schweizer, M
作者单位：Imperial College London; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We use probabilistic methods to study classical solutions for systems of interacting semilinear parabolic partial differential equations. In a modeling framework for a financial market with interacting Ito and point processes, such PDEs are shown to provide a natural description for the solution of hedging and valuation problems for contingent claims with a recursive payoff structure.
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作者：Rasonyi, M; Stettner, L
作者单位：HUN-REN; HUN-REN Institute for Computer Science & Control; Hungarian Academy of Sciences; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are constructed using optimal strategies.
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作者：Mandjes, M; Van Uitert, M
作者单位：Centrum Wiskunde & Informatica (CWI); University of Twente; Vrije Universiteit Amsterdam
摘要：This paper considers Gaussian flows multiplexed in a queueing network. A single node being a useful but often incomplete setting, we examine more advanced models. We focus on a (two-node) tandem queue, fed by a large number of Gaussian inputs. With service rates and buffer sizes at both nodes scaled appropriately, Schilder's sample-path large-deviations theorem can be applied to calculate the asymptotics of the overflow probability of the second queue. More specifically, we derive a lower boun...
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作者：Ata, B; Harrison, JM; Shepp, LA
作者单位：Northwestern University; Rutgers University System; Rutgers University New Brunswick; Stanford University
摘要：A system manager dynamically controls a diffusion process Z that lives in a finite interval [0, b]. Control takes the form of a negative drift rate 0 that is chosen from a fixed set A of available values. The controlled process evolves according to the differential relationship dZ = dX - theta (Z) dt + dL - dU, where X is a (0, sigma) Brownian motion, and L and U are increasing processes that enforce a lower reflecting barrier at Z = 0 and an upper reflecting barrier at Z = b, respectively. Th...
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作者：Egloff, D
摘要：We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical learning problem. Within this setup we apply deviation inequalities for suprema of empirical processes to derive consistency criteria, and to estimate the convergence rate and sample complexity. Our results strengthen and extend earlier results obtained by C...
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作者：Lambert, A
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Sorbonne Universite; Sorbonne Universite
摘要：In order to model random density-dependence in population dynamics, we construct the random analogue of the well-known logistic process in the branching process' framework. This density-dependence corresponds to intraspecific competition pressure, which is ubiquitous in ecology, and translates mathematically into a quadratic death rate. The logistic branching process, or LB-process, can thus be seen as (the mass of) a fragmentation process (corresponding to the branching mechanism) combined wi...
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作者：Dupuis, P; Wang, H
作者单位：Brown University
摘要：We consider the problem of optimal stopping for a one-dimensional diffusion process. Two classes of admissible stopping times are considered. The first class consists of all nonanticipating stopping times that take values in [0, ∞], while the second class further restricts the set of allowed values to the discrete grid {nh: n = 0, 1, 2,..., ∞} for some parameter h > 0. The value functions for the two problems are denoted by V(x) and V-h(x), respectively. We identify the rate of convergence o...
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作者：Fort, G; Roberts, GO
作者单位：Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Lancaster University
摘要：We derive sufficient conditions for subgeometric f-ergodicity of strongly Markovian processes. We first propose a criterion based on modulated moment of some delayed return-time to a petite set. We then formulate a criterion for polynomial f-ergodicity in terms of a drift condition on the generator. Applications to specific processes are considered, including Langevin tempered diffusions on R-n and storage models.
