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作者：Muller, Tobias; Spoehel, Reto
作者单位：Utrecht University
摘要：The random geometric graph is obtained by sampling n points from the unit square (uniformly at random and independently), and connecting two points whenever their distance is at most r, for some given r = r(n). We consider the following variation on the random geometric graph: in each of n rounds in total, a player is offered two random points from the unit square, and has to select exactly one of these two points for inclusion in the evolving geometric graph. We study the problem of avoiding ...
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作者：Cerf, Raphael
作者单位：Universite Paris Saclay
摘要：We pursue the task of developing a finite population counterpart to Eigen's model. We consider the classical Wright-Fisher model describing the evolution of a population of size m of chromosomes of length l over an alphabet of cardinality kappa. The mutation probability per locus is q. The replication rate is sigma > 1 for the master sequence and 1 for the other sequences. We study the equilibrium distribution of the process in the regime where l -> +infinity, m -> +infinity, q -> 0, l(q) -> a...
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作者：Sturm, Anja; Swart, Jan M.
作者单位：University of Gottingen; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
摘要：In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring (cooperative branching), and particles that land on an occupied site merge with the particle present on that site (coalescence). We show that the system undergoes a phase transition as the branching rate is increased. For small branching rates, the upper invariant law is trivial, and the process started with finitely many particles a.s. ends ...
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作者：Yu, Xiang
作者单位：University of Michigan System; University of Michigan
摘要：This paper studies the continuous time utility maximization problem on consumption with addictive habit formation in incomplete semimartingale markets. Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into a time-separable utility maximization problem with a shadow random endowment on the product space L-+(0) (Omega x [0, T], O, (P) over bar). Existence and uniqueness of the optimal solution are established using convex duality approac...
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作者：Yogeshwaran, D.; Adler, Robert J.
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; Technion Israel Institute of Technology
摘要：There has been considerable recent interest, primarily motivated by problems in applied algebraic topology, in the homology of random simplicial complexes. We consider the scenario in which the vertices of the simplices are the points of a random point process in R-d, and the edges and faces are determined according to some deterministic rule, typically leading to Cech and Vietoris-Rips complexes. In particular, we obtain results about homology, as measured via the growth of Beth numbers, when...
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作者：Chhita, Sunil; Johansson, Kurt; Young, Benjamin
作者单位：University of Bonn; Royal Institute of Technology; University of Oregon
摘要：We study random domino filings of the Aztec diamond with different weights for horizontal and vertical dominoes. A domino tiling of an Aztec diamond can also be described by a particle system which is a determinantal process. We give a relation between the correlation kernel for this process and the inverse Kasteleyn matrix of the Aztec diamond. This gives a formula for the inverse Kasteleyn matrix which generalizes a result of Helfgott. As an application, we investigate the asymptotics of the...
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作者：Andrieu, Christophe; Vihola, Matti
作者单位：University of Bristol; University of Oxford
摘要：We study convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms (Andrieu and Roberts [Ann. Statist. 37 (2009) 697-725]). We find that the asymptotic variance of the pseudo-marginal algorithm is always at least as large as that of the marginal algorithm. We show that if the marginal chain admits a (right) spectral gap and the weights (normalised estimates of the target density) are uniformly bounded, then the pseudo-marginal chain has a spectral gap. In many cases, a simi...
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作者：Lorig, Matthew; Pagliarani, Stefano; Pascucci, Andrea
作者单位：Princeton University; Institut Polytechnique de Paris; Ecole Polytechnique; University of Bologna
摘要：We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local volatility, local default intensity and a locally dependent Levy measure. Generalizing and extending the novel adjoint expansion technique of Pagliarani, Pascucci and Riga [SIAM J. Financial Math. 4 (2013) 265-296], we derive a family of asymptotic expansions for the transition density of the underlying as well as for...
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作者：Durrett, Rick; Zhang, Yuan
作者单位：Duke University
摘要：In this paper, we consider two attractive stochastic spatial models in which each site can be in state 0, 1 or 2: Krone's model in which 0 = vacant, 1 = juvenile and 2 = a mature individual capable of giving birth, and the Staver-Levin forest model in which 0 = grass, 1 = sapling and 2 = tree. Our first result shows that if (0, 0) is an unstable fixed point of the mean-field ODE for densities of 1's and 2's then when the range of interaction is large, there is positive probability of survival ...
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作者：Guasoni, Paolo; Rasonyi, Miklos
作者单位：Boston University; Dublin City University; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of Edinburgh
摘要：In a continuous-time model with multiple assets described by cadlag processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices arbitrarily unfavorable for high trading intensity. Such frictions induce a duality between feasible trading strategies and shadow execution prices with a martingale measure. Utility maximizing strategies exist even if arbitrage is present, because it is not scalab...
