-
作者：Terasawa, Yutaka; Yoshida, Nobuo
作者单位：University of Tokyo; Kyoto University
摘要：We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force. Here the extra stress tensor of the fluid is given by a polynomial of degree p - 1 of the rate of strain tensor, while the colored noise is considered as a random force. We investigate the existence and the uniqueness of weak solutions to this SPDE.
-
作者：Richou, Adrien
作者单位：Universite de Rennes
摘要：This article deals with the numerical resolution of Markovian backward stochastic differential equations (BSDEs) with drivers of quadratic growth with respect to z and bounded terminal conditions. We first show some bound estimates on the process Z and we specify the Zhang's path regularity theorem. Then we give a new time discretization scheme with a nonuniform time net for such BSDEs and we obtain an explicit convergence rate for this scheme.
-
作者：Guo, Xianping; Song, Xinyuan
作者单位：Sun Yat Sen University; Chinese University of Hong Kong
摘要：This paper is devoted to studying constrained continuous-time Markov decision processes (MDPs) in the class of randomized policies depending on state histories. The transition rates may be unbounded, the reward and costs are admitted to be unbounded from above and from below, and the state and action spaces are Polish spaces. The optimality criterion to be maximized is the expected discounted rewards, and the constraints can be imposed on the expected discounted costs. First, we give condition...
-
作者：Faller, Andreas; Rueschendorf, Ludger
作者单位：University of Freiburg
摘要：In this paper, we consider multistopping problems for finite discrete time sequences X1, ... , X-n. m-stops are allowed and the aim is to maximize the expected value of the best of these m stops. The random variables are neither assumed to be independent not to be identically distributed. The basic assumption is convergence of a related imbedded point process to a continuous time Poisson process in the plane, which serves as a limiting model for the stopping problem. The optimal m-stopping cur...
-
作者：Berestycki, J.; Harris, S. C.; Kyprianou, A. E.
作者单位：Sorbonne Universite; Universite Paris Cite; University of Bath
摘要：We formulate the notion of the classical Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) reaction diffusion equation associated with a homogeneous conservative fragmentation process and study its traveling waves. Specifically, we establish existence, uniqueness and asymptotics. In the spirit of classical works such as McKean [Comm. Pure Appl. Math. 28 (1975) 323-331] and [Comm. Pure Appl. Math. 29 (1976) 553-554], Neveu [In Seminar on Stochastic Processes (1988) 223-242 Birkh user] and Chauvin [...
-
作者：Bai, Z. D.; Liu, H. X.; Wong, W. K.
作者单位：Northeast Normal University - China; Northeast Normal University - China; National University of Singapore; Hong Kong Baptist University
摘要：Let S(n) = 1/nX(n)X*(n) where X(n) = {X(ij)} is a p x n matrix with i.i.d. complex standardized entries having finite fourth moments. Let Y(n)(t(1), t(2), sigma) = root p(x(n)(t(1))*(S(n) + sigma I)(-1)x(n)(t(2)) - x(n)(t(1))*x(n)(t(2)) m(n)(sigma)) in which sigma > 0 and m(n)(sigma) = integral dF(yn)(x)/x+sigma where F(yn)(x) is the Marcenko-Pastur law with parameter y(n) = p/n; which converges to a positive constant as n -> infinity, and x(n)(t(1)) and x(n)(t(2)) are unit vectors in C(p), ha...
-
作者：Jacka, Saul; Warren, Jon; Windridge, Peter
作者单位：University of Warwick
摘要：Suppose we have three independent copies of a regular diffusion on [0, 1] with absorbing boundaries. Of these diffusions, either at least two are absorbed at the upper boundary or at least two at the lower boundary. In this way, they determine a majority decision between 0 and 1. We show that the strategy that always runs the diffusion whose value is currently between the other two reveals the majority decision whilst minimizing the total time spent running the processes.
-
作者：Kanoria, Yashodhan; Montanari, Andrea
作者单位：Stanford University; Stanford University
摘要：A voter sits on each vertex of an infinite tree of degree k, and has to decide between two alternative opinions. At each time step, each voter switches to the opinion of the majority of her neighbors. We analyze this majority process when opinions are initialized to independent and identically distributed random variables. In particular, we bound the threshold value of the initial bias such that the process converges to consensus. In order to prove an upper bound, we characterize the process o...
-
作者：Appuhamillage, Thilanka; Bokil, Vrushali; Thomann, Enrique; Waymire, Edward; Wood, Brian
作者单位：Oregon State University; Oregon State University
-
作者：Chen, Xinfu; Cheng, Lan; Chadam, John; Saunders, David
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; State University of New York (SUNY) System; SUNY Fredonia; University of Waterloo
摘要：We study the inverse boundary crossing problem for diffusions. Given a diffusion process X-t, and a survival distribution p on [0,8), we demonstrate that there exists a boundary b(t) such that p(t) = P [tau > t], where t is the first hitting time of X-t to the boundary b(t). The approach taken is analytic, based on solving a parabolic variational inequality to find b. Existence and uniqueness of the solution to this variational inequality were proven in earlier work. In this paper, we demonstr...
