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作者：Baer, Michael; Duraj, Jetlir; Wachtel, Vitali
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; University of Bielefeld
摘要：Let S (n) be a centered random walk with finite second moment. We con-sider the integrated random walk T (n) = S(0) + S(1) + center dot center dot center dot + S(n). We prove invariance principles for the meander and for the bridge of this process, un-der the condition that the integrated random walk remains positive. Further-more, we prove the functional convergence of its Doob's h-transform to the h-transform of the Kolmogorov diffusion conditioned to stay positive.
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作者：Bose, Shreya; Ekren, Ibrahim
作者单位：State University System of Florida; Florida State University
摘要：We show that the problem of existence of equilibrium in Kyle's con-tinuous time insider trading model can be tackled by considering a forward -backward system coupled via an optimal transport type constraint at maturity. The forward component is a stochastic differential equation representing an endogenously determined state variable and the backward component is a quasilinear parabolic equation representing the pricing function. By obtain-ing a stochastic representation for the solution of su...
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作者：Zhou, Jianjun
作者单位：Northwest A&F University - China
摘要：In this article a notion of viscosity solutions is introduced for second -order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic differential equations. We identify the value functional of optimal control problems as unique viscosity solution to the associated PHJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions and satisfies a stabilit...
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作者：Popovic, Lea; Veber, Amandine
作者单位：Concordia University - Canada; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：We propose a novel measure valued process which models the behaviour of chemical reaction networks in spatially heterogeneous systems. It models reaction dynamics between different molecular species and continuous movement of molecules in space. Reactions rates at a spatial location are proportional to the mass of different species present locally and to a location specific chemical rate, which may be a function of the local or global species mass as well. We obtain asymptotic limits for the p...
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作者：Chen, Yong; Duan, Jinqiao; Gao, Hongjun
作者单位：Zhejiang Sci-Tech University; Illinois Institute of Technology; Southeast University - China
摘要：We study the global well-posedness and wave-breaking phenomenon for the stochastic rotation-two-component Camassa-Holm (R2CH) system. First, we find a Hamiltonian structure of the R2CH system and use the stochastic Hamiltonian to derive the stochastic R2CH system. Then, we establish the local well-posedness of the stochastic R2CH system using a dispersion-dissipation approximation system and the regularization method. We also show a precise blow-up criterion for the stochastic R2CH system. Mor...
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作者：Cosco, Clement; Nakajima, Shuta
作者单位：Weizmann Institute of Science; Meiji University
摘要：Consider the first passage percolation on the d-dimensional lattice Z(d) with identical and independent weight distributions and the first passage time T. In this paper, we study the upper tail large deviations P(T(0, nx) > n(mu + xi)), for xi > 0 and x not equal 0 with a time constant mu, for weights that sat-isfy a tail assumption P(tau e > t) asymptotic to beta exp (-alpha t(r)). When r <= 1 (this includes the well-known Eden growth model), we show that the upper tail large deviation decays...
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作者：Olesker-taylor, S. A. M.
作者单位：University of Bath
摘要：We establish cutoff for a natural random walk (RW) on the set of per-fect matchings (PMs), based on rewiring. An n-PM is a pairing of 2n ob-jects. The k -PM RW selects k pairs uniformly at random, disassociates the corresponding 2k objects, then chooses a new pairing on these 2k objects uniformly at random. The equilibrium distribution is uniform over all n-PMs. The 2-PM RW was first introduced by Diaconis and Holmes (Proc. Natl. Acad. Sci. USA 95 (1998) 14600-14602; Electron. J. Probab. 7 (20...
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作者：Feng, Xinwei; Hu, Ying; Huang, Jianhui
作者单位：Shandong University; Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); Hong Kong Polytechnic University
摘要：This paper aims to systematically solve stochastic team optimization of a large-scale system, in a linear-quadratic-Gaussian framework. Concretely, the underlying large-scale system involves considerable weakly coupled co-operative agents for which the individual admissible controls: (i) enter the diffusion terms, (ii) are constrained in some closed-convex subsets and (iii) subject to a general partial decentralized information structure. A more im-portant but serious feature: (iv) all agents ...
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作者：Claisse, Julien; Ren, Zhenjie; Tan, Xiaolu
作者单位：Universite PSL; Universite Paris-Dauphine; Chinese University of Hong Kong
摘要：Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empir-ical distribution. In the classical setting, the number of players is large but fixed throughout the game. However, in various applications, such as popu-lation dynamics or economic growth, the number of players can vary across time and this may lead to different Nash equilibria. In order to account for this evolution, we introduce a branching mechanism ...
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作者：Miller, Luke; Pitters, Helmut H.
作者单位：University of Oxford; University of California System; University of California Berkeley
摘要：We quantify the behaviour at large scales of the beta coalescent Pi = {Pi(t), t >= 0} with parameters a, b > 0. Specifically, we study the rescaled block size spectrum of Pi(t) and of its restriction Pi(n)(t) to {1, ... , n}. Our main result is a law of large numbers type of result if Pi comes down from infinity. In the case of Kingman's coalescent the derivation of this so-called hydrodynamic limit has been known since the work of Smoluchowski (Z. Phys. 17 (1916) 557-585). We extend Smoluchow...
