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  • JOURNAL ARTICLE
    Crisan D, McMurray E, 2018,

    Smoothing properties of McKean–Vlasov SDEs

    , Probability Theory and Related Fields, Vol: 171, Pages: 97-148, ISSN: 0178-8051

    © 2017, The Author(s). In this article, we develop integration by parts formulae on Wiener space for solutions of SDEs with general McKean–Vlasov interaction and uniformly elliptic coefficients. These integration by parts formulae hold both for derivatives with respect to a real variable and derivatives with respect to a measure understood in the sense of Lions. They allows us to prove the existence of a classical solution to a related PDE with irregular terminal condition. We also develop bounds for the derivatives of the density of the solutions of McKean–Vlasov SDEs.

  • JOURNAL ARTICLE
    Crisan D, Míguez J, 2018,

    Nested particle filters for online parameter estimation in discrete-time state-space Markov models

    , Bernoulli, Vol: 24, Pages: 2429-2460, ISSN: 1350-7265

    © 2018 ISI/BS. We address the problem of approximating the posterior probability distribution of the fixed parameters of a state-space dynamical system using a sequential Monte Carlo method. The proposed approach relies on a nested structure that employs two layers of particle filters to approximate the posterior probability measure of the static parameters and the dynamic state variables of the system of interest, in a vein similar to the recent “sequential Monte Carlo square” (SMC2) algorithm. However, unlike the SMC2scheme, the proposed technique operates in a purely recursive manner. In particular, the computational complexity of the recursive steps of the method introduced herein is constant over time. We analyse the approximation of integrals of real bounded functions with respect to the posterior distribution of the system parameters computed via the proposed scheme. As a result, we prove, under regularity assumptions, that the approximation errors vanish asymptotically in Lp(p ≥ 1) with convergence rate proportional to1N+1M, where N is the number of Monte Carlo samples in the parameter space and N × M is the number of samples in the state space. This result also holds for the approximation of the joint posterior distribution of the parameters and the state variables. We discuss the relationship between the SMC2algorithm and the new recursive method and present a simple example in order to illustrate some of the theoretical findings with computer simulations.

  • JOURNAL ARTICLE
    Davis M, Obloj J, Siorpaes P, 2018,

    Pathwise stochastic calculus with local times

    , ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, Vol: 54, Pages: 1-21, ISSN: 0246-0203
  • JOURNAL ARTICLE
    Gulisashvili A, Horvath B, Jacquier A, 2018,

    Mass at zero in the uncorrelated SABR model and implied volatility asymptotics

    , Quantitative Finance, Vol: 18, Pages: 1753-1765, ISSN: 1469-7688

    © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group. We study the mass at the origin in the uncorrelated stochastic alpha, beta, rho stochastic volatility model and derive several tractable expressions, in particular when time becomes small or large. As an application—in fact the original motivation for this paper—we derive small-strike expansions for the implied volatility when the maturity becomes short or large. These formulae, by definition arbitrage free, allow us to quantify the impact of the mass at zero on existing implied volatility approximations, and in particular how correct/erroneous these approximations become.

  • JOURNAL ARTICLE
    Olofsson S, Deisenroth MP, Misener R, 2018,

    Design of Experiments for Model Discrimination using Gaussian Process Surrogate Models

    , Vol: 44, Pages: 847-852, ISSN: 1570-7946

    © 2018 Elsevier B.V. Given rival mathematical models and an initial experimental data set, optimal design of experiments for model discrimination discards inaccurate models. Model discrimination is fundamentally about finding out how systems work. Not knowing how a particular system works, or having several rivalling models to predict the behaviour of the system, makes controlling and optimising the system more difficult. The most common way to perform model discrimination is by maximising the pairwise squared difference between model predictions, weighted by measurement noise and model uncertainty resulting from uncertainty in the fitted model parameters. The model uncertainty for analytical model functions is computed using gradient information. We develop a novel method where we replace the black-box models with Gaussian process surrogate models. Using the surrogate models, we are able to approximately marginalise out the model parameters, yielding the model uncertainty. Results show the surrogate model method working for model discrimination for classical test instances.

  • JOURNAL ARTICLE
    Wilson JT, Hutter F, Deisenroth MP, 2018,

    Maximizing acquisition functions for Bayesian optimization.

    , CoRR, Vol: abs/1805.10196
  • JOURNAL ARTICLE
    Abdulle A, Pavliotis GA, Vaes U, 2017,

    Spectral Methods for Multiscale Stochastic Differential Equations

    , SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, Vol: 5, Pages: 720-761, ISSN: 2166-2525
  • CONFERENCE PAPER
    Amiri MM, Gunduz D, 2017,

    Decentralized Caching and Coded Delivery over Gaussian Broadcast Channels

    , IEEE International Symposium on Information Theory (ISIT), Publisher: IEEE, Pages: 2785-2789
  • JOURNAL ARTICLE
    Ananova A, Cont R, 2017,

    Pathwise integration with respect to paths of finite quadratic variation

    , Journal des Mathematiques Pures et Appliquees, Vol: 107, Pages: 737-757, ISSN: 0021-7824

    © 2016 The Author(s) We study a pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums for gradient-type integrands. We show that the integral satisfies a pathwise isometry property, analogous to the well-known Ito isometry for stochastic integrals. This property is then used to represent the integral as a continuous map on an appropriately defined vector space of integrands. Finally, we obtain a pathwise ‘signal plus noise’ decomposition for regular functionals of an irregular path with non-vanishing quadratic variation, as a unique sum of a pathwise integral and a component with zero quadratic variation.

  • JOURNAL ARTICLE
    Arulkumaran K, Deisenroth MP, Brundage M, Bharath AAet al., 2017,

    A brief survey of deep reinforcement learning

    , IEEE Signal Processing Magazine, Vol: 34, Pages: 26-38, ISSN: 1053-5888

    Deep reinforcement learning (DRL) is poised to revolutionize the field of artificial intelligence (AI) and represents a step toward building autonomous systems with a higherlevel understanding of the visual world. Currently, deep learning is enabling reinforcement learning (RL) to scale to problems that were previously intractable, such as learning to play video games directly from pixels. DRL algorithms are also applied to robotics, allowing control policies for robots to be learned directly from camera inputs in the real world. In this survey, we begin with an introduction to the general field of RL, then progress to the main streams of value-based and policy-based methods. Our survey will cover central algorithms in deep RL, including the deep Q-network (DQN), trust region policy optimization (TRPO), and asynchronous advantage actor critic. In parallel, we highlight the unique advantages of deep neural networks, focusing on visual understanding via RL. To conclude, we describe several current areas of research within the field.

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