1,721,064 research outputs found
Constrained BSDEs driven by a non-quasi-left-continuous random measure and optimal control of PDMPs on bounded domains
No full textWe consider an optimal control problem for piecewise deterministic Markov processes (PDMPs) on a bounded state space. A pair of controls acts continuously on the deterministic fow and on the two transition measures (in the interior and from the boundary of the domain) describing the jump dynamics of the process. For this class of control problems, the value function can be characterized as the unique viscosity solution to the corresponding fully nonlinear Hamilton-Jacobi-Bellman equation with a nonlocal type boundary condition. By means of the recent control randomization method, we are able to provide a probabilistic representation for the value function in terms of a constrained backward stochastic diferential equation (BSDE), known as the nonlinear Feynman-Kac formula. This result considerably extends the existing literature, where only the case with no jumps from the boundary is considered. The additional boundary jump mechanism is described in terms of a non-quasi-left-continuous random measure and induces predictable jumps in the PDMP's dynamics. The existence and uniqueness results for BSDEs driven by such a random measure are nontrivial, even in the unconstrained case, as emphasized in the recent work [E. Bandini, Electron. Commun. Probab., 20 (2015), pp. 1-13]
Existence and uniqueness for BSDEs driven by a general random measure, possibly non quasi-left-continuous
Full text linkWe study the following backward stochastic differential equation on finite time horizon driven by an integer-valued random measure ц on R+ × E, where E is a Lusin space, with compensator v(dt, dx) = dAt Øt(dx): The generator f satisfies, as usual, a uniform Lipschitz condition with respect to its last two arguments. In the literature, the existence and uniqueness for the above equation in the present general setting has only been established when A is continuous or deterministic. The general case, i.e. A is a right-continuous nondecreasing predictable process, is addressed in this paper
Optimal Control of Infinite-Dimensional Piecewise Deterministic Markov Processes: A BSDE Approach. Application to the Control of an Excitable Cell Membrane
Full text linkIn this paper we consider the optimal control of Hilbert space-valued infinite-dimensional Piecewise Deterministic Markov Processes (PDMP) and we prove that the corresponding value function can be represented via a Feynman–Kac type formula through the solution of a constrained Backward Stochastic Differential Equation. A fundamental step consists in showing that the corresponding integro-differential Hamilton–Jacobi–Bellman equation has a unique viscosity solution, by proving a suitable comparison theorem. We apply our results to the control of a PDMP Hodgkin-Huxley model with spatial component
Stochastic filtering of a pure jump process with predictable jumps and path-dependent local characteristics
Full text linkThe objective of this paper is to study the filtering problem for a system of partially observable processes (X, Y), where X is a non-Markovian pure jump process representing the signal and Y is a general jump diffusion which provides observations. Our model covers the case where both processes are not necessarily quasi left-continuous, allowing them to jump at predictable stopping times. By introducing the Markovian version of the signal, we are able to compute an explicit equation for the filter via the innovations approach
Optimal control of Piecewise Deterministic Markov Processes: a BSDE representation of the value function
Full text linkWe consider an infinite-horizon discounted optimal control problem for piecewise deterministic Markov processes, where a piecewise open-loop control acts continuously on the jump dynamics and on the deterministic flow. For this class of control problems, the value function can in general be characterized as the unique viscosity solution to the corresponding Hamilton−Jacobi−Bellman equation. We prove that the value function can be represented by means of a backward stochastic differential equation (BSDE) on infinite horizon, driven by a random measure and with a sign constraint on its martingale part, for which we give existence and uniqueness results. This probabilistic representation is known as nonlinear Feynman−Kac formula. Finally we show that the constrained BSDE is related to an auxiliary dominated control problem, whose value function coincides with the value function of the original non-dominated control problem
A nonlinear Bismut–Elworthy formula for HJB equations with quadratic Hamiltonian in Banach spaces
Full text linkWe consider a Backward Stochastic Differential Equation (BSDE for short) in a Markovian framework for the pair of processes (Y, Z), with generator with quadratic growth with respect to Z. The forward equation is an evolution equation in an abstract Banach space. We prove an analogue of the Bismut–Elworty formula when the diffusion operator has a pseudo-inverse not necessarily bounded and when the generator has quadratic growth with respect to Z. In particular, our model covers the case of the heat equation in space dimension greater than or equal to 2. We apply these results to solve semilinear Kolmogorov equations in Banach spaces for the unknown v, with nonlinear term with quadratic growth with respect to ∇ v and final condition only bounded and continuous, and to solve stochastic optimal control problems with quadratic growth
A nonlinear Bismut–Elworthy formula for HJB equations with quadratic Hamiltonian in Banach spaces
Full text linkWe consider a Backward Stochastic Differential Equation (BSDE for short) in a Markovian framework for the pair of processes (Y, Z), with generator with quadratic growth with respect to Z. The forward equation is an evolution equation in an abstract Banach space. We prove an analogue of the Bismut–Elworty formula when the diffusion operator has a pseudo-inverse not necessarily bounded and when the generator has quadratic growth with respect to Z. In particular, our model covers the case of the heat equation in space dimension greater than or equal to 2. We apply these results to solve semilinear Kolmogorov equations in Banach spaces for the unknown v, with nonlinear term with quadratic growth with respect to ∇ v and final condition only bounded and continuous, and to solve stochastic optimal control problems with quadratic growth
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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