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Mathematical Models of Weighted Monte Carlo Methods
Using Information About the Solution
Nonlinear Theory of Optimization
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absorption approximate arbitrary assume asymptotics average boundary calculated coefficient collision estimate computational condition constructed convergence correlation function corresponding cross section defined Denote derivatives direct simulation Dirichlet problem domain equal evaluate example finite flux free length G.A. Mikhailov Gaussian importance sampling inequality integral equations integral operator isotropic iterative kernel layer Lemma Let us consider Markov chain Math matrix medium minimal minimax Monte Carlo algorithms Monte Carlo estimates Monte Carlo Methods Neumann series nonnegative Note obtain one-dimensional distribution optical optimal p(Kp parameter particle plane possible Proof quantity radiative transfer random field random value random variable random vector relation repetition method replaced respect satisfied scattering indicatrix space spectral spectral radius system of integral Theorem tion trajectory transfer equation transfer theory transition density uniformly variance vector algorithm vector estimate walk on spheres weak convergence weighted estimates weighted Monte Carlo zero