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作者：Kloeckner, Benoit
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：Applying quantitative perturbation theory for linear operators, we prove nonasymptotic bounds for Markov chains whose transition kernel has a spectral gap in an arbitrary Banach algebra of functions X. The main results are concentration inequalities and Berry-Esseen bounds, obtained assuming neither reversibility nor warm start hypothesis: the law of the first term of the chain can be arbitrary. The spectral gap hypothesis is basically a uniform X - ergodicity hypothesis, and when X consist in...
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作者：Wang, Andi Q.; Kolb, Martin; Roberts, Gareth O.; Steinsaltz, David
作者单位：University of Oxford; University of Paderborn; University of Warwick
摘要：This paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems. We prove natural sufficient conditions for the quasi-limiting distribution of a killed diffusion to coincide with a target density of interest. We also quantify the rate of convergence to quasi-stationarity by relating the killed diffusion to an appropriate Langevin diffusion. As an example, we consider in detail a killed Ornstein-Uhlenbeck process with Gaussian quasi-stationary d...
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作者：Keller-Ressel, Martin; Schmidt, Thorsten; Wardenga, Robert
作者单位：Technische Universitat Dresden; University of Freiburg; University of Freiburg
摘要：In this paper, we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting, times of jumps can be both inaccessible and predictable. To this end, we develop a general theory of finite dimensional affine semimartingales under very weak assumptions. We show that the corresponding semimartingale characteristics have affine form and that the conditional characteristic function can be represented with solutions to measure differential equation...
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作者：Hammond, Alan; Hegde, Milind
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We study a spatial model of random permutations on trees with a time parameter T > 0, a special case of which is the random stirring process. The model on trees was first analysed by Bjornberg and Ueltschi [Ann. Appl. Probab. 28 (2018) 2063-2082], who established the existence of infinite cycles for T slightly above a putatively identified critical value but left open behaviour at arbitrarily high values of T. We show the existence of infinite cycles for all T greater than a constant, thus cla...
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作者：Szpruch, Lukasz; Tan, Shuren; Tse, Alvin
作者单位：University of Edinburgh
摘要：The mean field limits of systems of interacting diffusions (also called stochastic interacting particle systems (SIPS)) have been intensively studied since McKean (Proc. Natl. Acad. Sci. USA 56 (1966) 1907-1911) as they pave a way to probabilistic representations for many important nonlinear/nonlocal PDEs. The fact that particles are not independent render classical variance reduction techniques not directly applicable, and consequently make simulations of interacting diffusions prohibitive. I...
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作者：Agazzi, Andrea; Dembo, Amir; Eckmann, Jean-Pierre
作者单位：Stanford University; Stanford University; University of Geneva; University of Geneva; University of Geneva; Duke University
摘要：We prove a sample path Large Deviation Principle (LDP) for a class of jump processes whose rates are not uniformly Lipschitz continuous in phase space. Building on it, we further establish the corresponding Wentzell-Freidlin (W-F) (infinite time horizon) asymptotic theory. These results apply to jump Markov processes that model the dynamics of chemical reaction networks under mass action kinetics, on a microscopic scale. We provide natural sufficient topological conditions for the applicabilit...
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作者：Gravner, Janko; Lyu, Hanbaek; Sivakoff, David
作者单位：University of California System; University of California Davis; University System of Ohio; Ohio State University
摘要：Fix a simple graph G = (V, E) and choose a random initial 3-coloring of vertices drawn from a uniform product measure. The 3-color cycle cellular automaton is a process in which at each discrete time step in parallel, every vertex with color i advances to the successor color (i + 1) mod 3 if in contact with a neighbor with the successor color, and otherwise retains the same color. In the Greenberg-Hastings model, the same update rule applies only to color 0, while other two colors automaticall...
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作者：Owada, Takashi
作者单位：Purdue University System; Purdue University
摘要：We investigate the topological dynamics of extreme sample clouds generated by a heavy tail distribution on R-d by establishing various limit theorems for Betti numbers, a basic quantifier of algebraic topology. It then turns out that the growth rate of the Betti numbers and the properties of the limiting processes all depend on the distance of the region of interest from the weak core, that is, the area in which random points are placed sufficiently densely to connect with one another. If the ...
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作者：Bandini, Elena; Cosso, Andrea; Fuhrman, Marco; Huyen Pham
作者单位：Luiss Guido Carli University; Polytechnic University of Milan; University of Milan; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Luiss Guido Carli University
摘要：We introduce a suitable backward stochastic differential equation (BSDE) to represent the value of an optimal control problem with partial observation for a controlled stochastic equation driven by Brownian motion. Our model is general enough to include cases with latent factors in mathematical finance. By a standard reformulation based on the reference probability method, it also includes the classical model where the observation process is affected by a Brownian motion (even in presence of a...
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作者：Pages, Gilles; Panloup, Fabien
作者单位：Sorbonne Universite; Universite d'Angers
摘要：We investigate a weighted multilevel Richardson-Romberg extrapolation for the ergodic approximation of invariant distributions of diffusions adapted from the one introduced in [Bernoulli 23 (2017) 2643-2692] for regular Monte Carlo simulation. In a first result, we prove under weak confluence assumptions on the diffusion, that for any integer R >= 2, the procedure allows us to attain a rate n(R/2R+1) whereas the original algorithm convergence is at a weak rate n(1/3). Furthermore, this is achi...
