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作者：Giacomin, Giambattista; Lacoin, Hubert
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We consider the lattice Gaussian free field in d + 1 dimensions, d = 3 or larger, on a large box (linear size N) with boundary conditions zero. On this field, two potentials are acting: one, that models the presence of a wall, penalizes the field when it enters the lower half space and one, the pinning potential, rewards visits to the proximity of the wall. The wall can be soft, that is, the field has a finite penalty to enter the lower half-plane, or hard, when the penalty is infinite. In gen...
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作者：Atar, Rami; Biswas, Anup; Kaspi, Haya; Ramanan, Kavita
作者单位：Technion Israel Institute of Technology; Indian Institute of Science Education & Research (IISER) Pune; Technion Israel Institute of Technology; Brown University
摘要：The Skorokhod map on the half-line has proved to be a useful tool for studying processes with nonnegativity constraints. In this work, we introduce a measure-valued analog of this map that transforms each element. of a certain class of cadlag paths that take values in the space of signed measures on [0, infinity) to a cadlag path that takes values in the space of nonnegative measures on [0, infinity) in such a way that for each x > 0, the path t (bar right arrow) zeta(t) [0, x] is transformed ...
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作者：Crane, Harry
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：Combinatorial Levy processes evolve on general state spaces of combinatorial structures, of which standard examples include processes on sets, graphs and n-ary relations and more general possibilities are given by processes on graphs with community structure and multilayer networks. In this setting, the usual Levy process properties of stationary, independent increments are defined in an unconventional way in terms of the symmetric difference operation on sets. The main theorems characterize b...
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作者：Claisse, Julien
作者单位：Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：In this paper, we aim to develop the stochastic control theory of branching diffusion processes where both the movement and the reproduction of the particles depend on the control. More precisely, we study the problem of minimizing the expected value of the product of individual costs penalizing the final position of each particle. In this setting, we show that the value function is the unique viscosity solution of a nonlinear parabolic PDE, that is, the Hamilton-Jacobi-Bellman equation corres...
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作者：Casanova, Adrian Gonzalez; Spano, Dario
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Warwick
摘要：A two-types, discrete-time population model with finite, constant size is constructed, allowing for a general form of frequency-dependent selection and skewed offspring distribution. Selection is defined based on the idea that individuals first choose a (random) number of potential parents from the previous generation and then, from the selected pool, they inherit the type of the fittest parent. The probability distribution function of the number of potential parents per individual thus parame...
