1,721,009 research outputs found
On the Backward Stochastic Riccati Equation in Infinite Dimensions
No full textThis paper deals with linear quadratic stochastic control problems in infinite-dimensional Hilbert space with random operator valued coefficients. This is certainly a classical problem, first treated by J.-M. Bismut [SIAM J. Control Optimization 14 (1976), no. 3, 419–444; MR0406663 (53 #10449)] for general finite-dimensional problems and later by N. U. Ahmed [SIAM J. Control Optim. 19 (1981), no. 3, 401–430; MR0613102 (82j:93054)] for infinite-dimensional problems involving unbounded random operator valued coefficients. Following a basic variational principle one can easily derive the necessary conditions for optimality. This approach gives rise to backward stochastic differential equations on infinite-dimensional spaces. The questions of existence, even uniqueness, and regularity properties of solutions of the associated operator Riccati equations are of fundamental importance. Such problems have been treated in [N. U. Ahmed, op. cit.] for operators based on the Gel′fand triple {V, H, V ∗}. In the paper under review the operators include a deterministic infinitesimal generator of a C0 semigroup and some bounded linear operator valued stochastic processes. The paper presents some interesting results on the existence and uniqueness of solutions of the stochastic Riccati equations. Conceptually one may consider this as the solution of the LQR problem in infinite-dimensional Hilbert space, though from a practical point of view this is far from it. It seems the authors have missed some earlier papers in the same area which we included here (see the papers cited above as well as [N. U. Ahmed, in Differential equations and applications, Vol. I, II (Columbus, OH, 1988), 13–19, Ohio Univ. Press, Athens, OH, 1989; MR1026110 (91h:60067)])
Existence of optimal stochastic controls and global solutions of forward-backward stochastic differential equations
No full textWe consider an optimal stochastic control problem, assuming Lipschitz conditions and allowing degeneracy of the diffusion coefficient, under some structural constraint on the state equation. We formulate the problem in the strong form; i.e., we fix the probability space. We relate
the value function and the feedback law to a forward-backward stochastic differential system. We prove existence and uniqueness of a global solution to the latter and deduce existence and, in some cases, uniqueness of an optimal control. To solve the (coupled) forward-backward system we use a priori estimates which follow from its control-theoretic interpretation
Backward stochastic differential equations in finite and infinite dimensions. Applications to optimal control and hedging.
No full textQuaderni del Dipartimento di Matematica , Universita' di Parma, n. 380
Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces
No full textSolutions of semilinear elliptic differential equations in infinite-dimensional spaces are obtained by means of forward and backward infinite-dimensional stochastic evolution equations. The backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition. Elliptic equations are intended in a mild sense, suitable also for applications to optimal control. We finally notice that, due to the lack of smoothing properties, the elliptic partial differential equation
considered here could not be treated by analytic methods
The Bismut-Elworthy formula for backward SDE's and applications to nonlinear Kolmogorov equations and control in infinite dimensional spaces
No full textNonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control
No full textDirect closure of an asymptomatic right coronary sinus of Valsalva aneurysm
No full textA 52-year-old man was referred for evaluation of palpitation. Transthoracic echocardiography revealed an extracardiac aneurysm of the right coronary sinus of Valsalva, and normal anatomy of the aortic valve with no regurgitation. Three-dimensional computed tomography confirmed the aneurysm with a diameter of 21 × 13.7 mm arising from the right coronary sinus of Valsalva under the right coronary artery. Surgical repair was performed without changing the normal anatomy of the aortic valve, preserving the right coronary ostium. Intraoperative and postoperative echocardiography showed complete closure of the aneurysm with normal functioning of the aortic valve.
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KEYWORDS: Aortic aneurysm; echocardiography; sinus of valsalv
Generalized directional gradients, backward stochastic differential equations and mild solutions of semilinear parabolic equations.
Full text linkWe study a forward-backward system of stochastic differential equations in an infinite-dimensional framework and its relationships with a semilinear parabolic differential equation on a Hilbert space, in the spirit of the approach of Pardoux-Peng. We prove that the stochastic system allows us to construct a unique solution of the parabolic equation in a suitable class of locally Lipschitz real functions. The parabolic equation is understood in a mild sense which requires the notion of a generalized directional gradient, that we introduce by a probabilistic approach and prove to exist for locally Lipschitz functions. The use of the generalized directional gradient allows us to cover various applications to option pricing problems and to optimal stochastic control problems (including control of delay equations and reaction - diffusion equations), where the lack of differentiability of the coefficients precludes differentiability of solutions to the associated parabolic equations of Black - Scholes or Hamilton-Jacobi-Bellman type
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
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