On the rate of convergence of finite-difference approximations for Bellmans equations with variable coefficients

By Nicolai V. Krylov. 2000

213 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6e6407da64ab42a411d996c0562c3d0afb11beae

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Viscosity Solutions for a System of Integro-PDEs and Connections to Optimal Switching and Control of Jump-Diffusion Processes (2010, background): “This is a dicult problem that remained open for a long time before the works of Krylov[32, 33 , 34] and Barles & Jakobsen [8, 9, 10].”
The Rate of Convergence of Finite-Difference Approximations for Parabolic Bellman Equations with Lipschitz Coefficients in Cylindrical Domains (2007, methodology): “We will be using the method of “shaking” the coefficients introduced in [16] and [ 17 ].”
AN OPTIMAL MARKOVIAN QUANTIZATION ALGORITHM FOR MULTI-DIMENSIONAL STOCHASTIC CONTROL PROBLEMS (2004, background): “1 We mention that recently, Krylov presents in [17] a different method for proving the convergence which also provides an estimate of the rate of convergence of finite difference approximations of Bellman’s equation.”
A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models (2005, unknown): “The following (see appendix) is a slightly improved version of a result in [22].”
CONTINUOUS DEPENDENCE ESTIMATES FOR VISCOSITY SOLUTIONS OF INTEGRO-PDES (2005, unknown): “The case of numerical methods is more difficult and some of the first results in that direction for the pure PDE version of the convex Bellman equation can be found in [7, 8, 32, 38].”
A control approach to robust utility maximization with logarithmic utility and time-consistent penalties (2007, background): “For convergence results of such numerical schemes see [20], Krylov [19], Barles and Jakobsen [2], and the references therein.”
A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs (2008, methodology): “The first result in the convex/concave case, with h = 1/27, was obtained by Krylov [K1], [ K2 ] using the stochastic control interpretation of the equation that is available in view of the convexity/concavity of F. Later Barles and Jacobsen [BJ1], [BJ2] improved the error to h = 1/5 by purely pde te”
ON THE RATE OF CONVERGENCE OF APPROXIMATION SCHEMES FOR BELLMAN EQUATIONS ASSOCIATED WITH OPTIMAL STOPPING TIME PROBLEMS (2003, methodology): “The first difficulty is handled using techniques introduced by Krylov in [17].”
On some recent aspects of stochastic control and their applications (2005, result): “There are also recent results on convergence rate for the finite difference approximation of the HJB equation in [ 57 ] and [6].”
On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations (2002, background): “This idea was already used by Krylov in the x-independent case.”