-
作者：Holden, Nina; Lyons, Russell
作者单位：Massachusetts Institute of Technology (MIT); Indiana University System; Indiana University Bloomington
摘要：In the trace reconstruction problem, an unknown bit string x is an element of {0, 1}(n) is sent through a deletion channel where each bit is deleted independently with some probability q is an element of (0, 1), yielding a contracted string (x) over tilde. How many i.i.d. samples of (x) over tilde are needed to reconstruct x with high probability? We prove that there exist x, y is an element of {0, 1}(n) such that at least cn(5/4)/root log n traces are required to distinguish between x and y f...
-
作者：Wu, Cong; Zhang, Jianfeng
作者单位：University of Southern California
摘要：The master equation is a type of PDE whose state variable involves the distribution of certain underlying state process. It is a powerful tool for studying the limit behavior of large interacting systems, including mean field games and systemic risk. It also appears naturally in stochastic control problems with partial information and in time inconsistent problems. In this paper we propose a novel notion of viscosity solution for parabolic master equations, arising mainly from control problems...
-
作者：Caye, Thomas; Herdegen, Martin; Muhle-Karbe, Johannes
作者单位：Dublin City University; University of Warwick; Imperial College London
摘要：We study portfolio choice with small nonlinear price impact on general market dynamics. Using probabilistic techniques and convex duality, we show that the asymptotic optimum can be described explicitly up to the solution of a nonlinear ODE, which identifies the optimal trading speed and the performance loss due to the trading friction. Previous asymptotic results for proportional and quadratic trading costs are obtained as limiting cases. As an illustration, we discuss how nonlinear trading c...
-
作者：Fang, Wei; Giles, Michael B.
作者单位：University of Oxford
摘要：This paper proposes an adaptive timestep construction for an Euler-Maruyama approximation of SDEs with nonglobally Lipschitz drift. It is proved that if the timestep is bounded appropriately, then over a finite time interval the numerical approximation is stable, and the expected number of timesteps is finite. Furthermore, the order of strong convergence is the same as usual, that is, order 1/2 for SDEs with a nonuniform globally Lipschitz volatility, and order 1 for Langevin SDEs with unit vo...
-
作者：Hermon, Jonathan; Ben Morris; Qin, Chuan; Sly, Allan
作者单位：University of Cambridge; University of California System; University of California Davis; Princeton University
摘要：Given an infinite connected regular graph G = (V, E), place at each vertex Poisson(lambda) walkers performing independent lazy simple random walks on G simultaneously. When two walkers visit the same vertex at the same time they are declared to be acquainted. We show that when G is vertex-transitive and amenable, for all lambda > 0 a.s. any pair of walkers will eventually have a path of acquaintances between them. In contrast, we show that when G is nonamenable (not necessarily transitive) the...
