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作者：Fuhrman, Marco; Huyen Pham
作者单位：Polytechnic University of Milan; Universite Paris Cite
摘要：We study optimal stochastic control problems for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients and gain functionals are path-dependent, and importantly we do not make any ellipticity assumptions on the SDE. We develop a control randomization approach and prove that the value function can be reformulated under a family of dominated measures on an enlarged filtered probability space. This value function is then characterized by a backward SDE with...
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作者：Kardaras, Constantinos
作者单位：University of London; London School Economics & Political Science
摘要：In this paper, a study of random times on filtered probability spaces is undertaken. The main message is that, as long as distributional properties of optional processes up to the random time are involved, there is no loss of generality in assuming that the random time is actually a randomised stopping time. This perspective has advantages in both the theoretical and practical study of optional processes up to random times. Applications are given to financial mathematics, as well as to the stu...
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作者：Arapstathis, Art; Biswas, Anup; Pang, Guodong
作者单位：University of Texas System; University of Texas Austin; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We study a dynamic scheduling problem for a multi-class queueing network with a large pool of statistically identical servers. The arrival processes are Poisson, and service times and patience times are assumed to be exponentially distributed and class dependent. The optimization criterion is the expected long time average (ergodic) of a general (nonlinear) running cost function of the queue lengths. We consider this control problem in the Halfin-Whitt (QED) regime, that is, the number of serv...
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作者：Bertacchi, Daniela; Zucca, Fabio
作者单位：University of Milano-Bicocca; Polytechnic University of Milan
摘要：In this paper we prove that, under the assumption of quasi-transitivity, if a branching random walk on Z(d) survives locally (at arbitrarily large times there are individuals alive at the origin), then so does the same process when restricted to the infinite percolation cluster Coo of a supercritical Bernoulli percolation. When no more than k individuals per site are allowed, we obtain the k-type contact process, which can be derived from the branching random walk by killing all particles that...
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作者：Berti, Patrizia; Crimaldi, Irene; Pratelli, Luca; Rigo, Pietro
作者单位：Universita di Modena e Reggio Emilia; IMT School for Advanced Studies Lucca; University of Pavia
摘要：The three-parameter Indian buffet process is generalized. The possibly different role played by customers is taken into account by suitable (random) weights. Various limit theorems are also proved for such generalized Indian buffet process. Let L-n be the number of dishes experimented by the first n customers, and let (K) over bar (n)= (1/n) Sigma(n)(i=1) K-i where K-i is the number of dishes tried by customer i. The asymptotic distributions of L-n and (K) over bar (n), suitably centered and s...
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作者：Moyal, P.
作者单位：Universite de Technologie de Compiegne
摘要：We propose an explicit construction of a stationary solution for a stochastic recursion of the form X o theta = phi(X) on a partially-ordered Polish space, when the monotonicity of phi is not assumed. Under certain conditions, we show that an extension of the original probability space exists, on which a solution is well defined, and construct explicitly this extension using a randomized contraction technique. We then provide conditions for the existence of a solution on the original space. We...
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作者：Georgiou, Nicos; Joseph, Mathew; Khoshnevisan, Davar; Shiu, Shang-Yuan
作者单位：University of Sussex; University of Sheffield; Utah System of Higher Education; University of Utah; National Central University
摘要：Consider an infinite system partial derivative(t)u(t) (x) = (Lu-t) (x) + sigma (u(t) (x)) partial derivative(t) B-t (x) of interacting Ito diffusions, started at a nonnegative deterministic bounded initial profile. We study local and global features of the solution under standard regularity assumptions on the nonlinearity sigma. We will show that, locally in time, the solution behaves as a collection of independent diffusions. We prove also that the kth moment Lyapunov exponent is frequently o...
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作者：Lionnet, Arnaud; Dos Reis, Goncalo; Szpruch, Lukasz
作者单位：University of Oxford; University of Edinburgh
摘要：In this paper, we undertake the error analysis of the time discretization of systems of Forward Backward Stochastic Differential Equations (FBSDEs) with drivers having polynomial growth and that are also monotone in the state variable. We show with a counter-example that the natural explicit Euler scheme may diverge, unlike in the canonical Lipschitz driver case. This is due to the lack of a certain stability property of the Euler scheme which is essential to obtain convergence. However, a tho...
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作者：Dupuis, Paul; Spiliopoulos, Konstantinos; Zhou, Xiang
作者单位：Brown University; Boston University; City University of Hong Kong
摘要：We discuss importance sampling schemes for the estimation of finite time exit probabilities of small noise diffusions that involve escape from an equilibrium. A factor that complicates the analysis is that rest points are included in the domain of interest. We build importance sampling schemes with provably good performance both pre-asymptotically, that is, for fixed size of the noise, and asymptotically, that is, as the size of the noise goes to zero, and that do not degrade as the time horiz...
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作者：Zhu, Lingjiong
作者单位：New York University
摘要：Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, neuroscience and many other fields. In this paper, we study the large deviations for nonlinear Hawkes processes. The large deviations for linear Hawkes processes has been studied by Bordenave and Torrisi. In this paper, we prove first a large deviation principle for a special class of no...
