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作者：Costa, Manon
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We are interested in prey-predator communities where the predator population evolves much faster than the prey's (e.g., insect-tree communities). We introduce a piecewise deterministic model for these prey-predator communities that arises as a limit of a microscopic model when the number of predators goes to infinity. We prove that the process has a unique invariant probability measure and that it is exponentially ergodic. Further on, we rescale the predator dynamics in order to model predator...
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作者：Benaim, Michel; Lobry, Claude
作者单位：University of Neuchatel; Universite Cote d'Azur
摘要：We consider two-dimensional Lotka-Volterra systems in a fluctuating environment. Relying on recent results on stochastic persistence and piece wise deterministic Markov processes, we show that random switching between two environments that are both favorable to the same species can lead to the extinction of this species or coexistence of the two competing species.
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作者：Cerou, Frederic; Guyader, Arnaud
作者单位：Universite de Rennes; Universite de Rennes; Sorbonne Universite; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite de Rennes
摘要：Multilevel Splitting, also called Subset Simulation, is a Sequential Monte Carlo method to simulate realisations of a rare event as well as to estimate its probability. This article is concerned with the convergence and the fluctuation analysis of Adaptive Multilevel Splitting techniques. In contrast to their fixed level version, adaptive techniques estimate the sequence of levels on the fly and in an optimal way, with only a low additional computational cost. However, very few convergence res...
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作者：Podolskij, Mark; Yoshida, Nakahiro
作者单位：Aarhus University; Japan Science & Technology Agency (JST); Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
摘要：This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the Edgeworth expansion for power variation of diffusion processes. Our methodology relies on martingale embedding, Malliavin calculus and stable central limit theorems for semimartingales. Finally, we demonstrate the density expansion for Studentized statistics of p...
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作者：Forde, Martin; Kumar, Rohini
作者单位：University of London; King's College London; Wayne State University
摘要：We establish a large-time large deviation principle (LDP) for a general mean-reverting stochastic volatility model with nonzero correlation and sublinear growth for the volatility coefficient, using the Donsker-Varadhan [Comm. Pure Appl. Math. 36 (1983) 183-212] LDP for the occupation measure of a Feller process under mild ergodicity conditions. We verify that these conditions are satisfied when the process driving the volatility is an Ornstein Uhlenbeck (013) process with a perturbed (subline...
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作者：Ren, Zhenjie
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：This paper extends the recent work on path-dependent PDEs to elliptic equations with Dirichlet boundary conditions. We propose a notion of viscosity solution in the same spirit as [Ann. Probab. 44 (2016) 1212-1253, Part 1; Ekren, Touzi and Zhang (2016), Part 2], relying on the theory of optimal stopping under nonlinear expectation. We prove a comparison result implying the uniqueness of viscosity solution, and the existence follows from a Perron type construction using path-frozen PDEs. We als...
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作者：Brehier, Charles-Edouard; Gazeau, Maxime; Goudenege, Ludovic; Lelievre, Tony; Rousset, Mathias
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Claude Bernard Lyon 1; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; University of Toronto; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Gustave-Eiffel; Inria; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We introduce a generalization of the Adaptive Multilevel Splitting algorithm in the discrete time dynamic setting, namely when it is applied to sample rare events associated with paths of Markov chains. We build an estimator of the rare event probability (and of any nonnormalized quantity associated with this event) which is unbiased, whatever the choice of the importance function and the number of replicas. This has practical consequences on the use of this algorithm, which are illustrated th...
