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作者：Connor, Stephen B.; Kendall, Wilfrid S.
作者单位：University of Warwick
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作者：Hairer, M.; Stuart, A. M.; Voss, J.
作者单位：University of Warwick
摘要：In many applications, it is important to be able to sample paths of SDEs conditional on observations of various kinds. This paper studies SPDEs which solve such sampling problems. The SPDE may be viewed as an infinite-dimensional analogue of the Langevin equation used in finite-dimensional sampling. In this paper, conditioned nonlinear SDEs, leading to nonlinear SPDEs for the sampling, are studied. In addition, a class of preconditioned SPDEs is studied, found by applying a Green's operator to...
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作者：Jeanblanc, Monique; Kloeppel, Susanne; Miyahara, Yoshio
作者单位：Universite Paris Saclay; Nagoya City University; Technische Universitat Wien
摘要：Let L be a multidimensional Levy process under P in its own filtration. The p-minimal martingale measure Q(q) is defined as that equivalent local martingale measure for 8 (L) which minimizes the f(q)-divergence E[(dQ/dp)(q)] for fixed q epsilon (-infinity, 0) boolean OR (1, infinity). We give necessary and sufficient conditions for the existence of Qq and an explicit formula for its density. For q = 2, we relate the sufficient conditions to the structure condition and discuss when the former a...
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作者：MacPhee, Iain; Menshikov, Mikhail; Petritis, Dimitri; Popov, Serguei
作者单位：Durham University; Universidade de Sao Paulo; Universite de Rennes
摘要：We study a model of a polling system, that is, a collection of d queues with a single server that switches from queue to queue. The service time distribution and arrival rates change randomly every time a queue is emptied. This model is mapped to a mathematically equivalent model of a random walk with random choice of transition probabilities, a model which is of independent interest. All our results are obtained using methods from the constructive theory of Markov chains. We determine conditi...
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作者：Atar, Rami; Budhiraja, Amarjit; Williams, Ruth J.
作者单位：Technion Israel Institute of Technology; University of California System; University of California San Diego; University of North Carolina; University of North Carolina Chapel Hill
摘要：Given a closed, bounded convex set W subset of R-d with nonempty interior, we consider a control problem in which the state process W and the control process U satisfy [Graphics] where Z is a standard, multi-dimensional Brownian motion, nu, sigma epsilon C-0,C-1 (W), G is a fixed matrix, and w(o) epsilon w. The process U is locally of bounded variation and has increments in a given closed convex cone U C RP. Given g epsilon C(W), K epsilon R-P, and alpha > 0, consider the objective that is to ...
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作者：Caputo, Pietro; Faggionato, Alessandra
作者单位：Roma Tre University; Sapienza University Rome
摘要：We consider the random walk on a simple point process on R-d, d >= 2, whose jump rates decay exponentially in the alpha-power of jump length. The case alpha = 1 corresponds to the phonon-induced variable-range hopping in disordered solids in the regime of strong Anderson localization. Under mild assumptions on the point process, we show, for a epsilon (0, d), that the random walk confined to a cubic box of side L has a.s. Cheeger constant of order at least L-1 and mixing time of order L-2. For...
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作者：Guyon, Julien
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：We propose a general method to study dependent data in a binary tree, where an individual in one generation gives rise to two different offspring, one of type 0 and one of type 1, in the next generation. For any specific characteristic of these individuals, we assume that the characteristic is stochastic and depends on its ancestors' only through the mother's characteristic. The dependency structure may be described by a transition probability P (x, dy dz) which gives the probability that the ...
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作者：Blath, Jochen; Etheridge, Alison; Meredith, Mark
作者单位：Technical University of Berlin; University of Oxford
摘要：We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system models, which do not, at present, incorporate all of the competitive strategies that a population might adopt. The second is a simplification of the first, in which competition is only supposed to act within lattice sites and the total population size within ea...
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作者：Yu, Feng
作者单位：University of Oxford
摘要：We study dioccious (i.e., two-sex) branching particle system models, where there are two types of particles, modeling the male and female populations, and where birth of new particles requires the presence of both male and female particles. We show that stationary distributions of various dioecious branching particle models are nontrivial under certain conditions, for example, when there is sufficiently fast stirring.
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作者：Roellin, Adrian
作者单位：University of Zurich
摘要：It is shown that the method of exchangeable pairs introduced by Stein [Approximate Computation of Expectations (1986) IMS, Hayward, CA] for normal approximation can effectively be used for translated Poisson approximation. Introducing an additional smoothness condition, one can obtain approximation results in total variation and also in a local limit metric. The result is applied, in particular, to the anti-voter model on finite graphs as analyzed by Rinott and Rotar [Ann. Appl. Probab. 7 (199...
