Numerical Solution of Stochastic Differential Equations

By Peter E. Kloeden, Eckhard Platen. 1992

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Citations in the corpus

Heavy-flavour spectra in high-energy nucleus–nucleus collisions (2011, methodology): “Actually, the whole procedure depends on the discretization scheme employed in the numerical solution of (9), which belongs to the class of the stochastic differential equations [ 57 , 58].”
Estimation for discretely observed diffusions using transform functions (2003, methodology): “where R�i,n,�(�n,�n 1,X�n) is the corresponding remainder term, as follows from Kloeden & Platen (1999) .”
A numerical scheme for stochastic PDEs with Gevrey regularity (2004, methodology): “The easiest way to obtain higher order schemes is to apply an It ˆ o‐Taylor expansion (see [ 12 ]).”
Parameter estimation in stochastic grey-box models (2004, methodology): “SDEs may be interpreted both in the sense of Stratonovich and in the sense of Itô, but since the Stratonovich interpretation is less suitable for parameter estimation (Jazwinski, 1970; Astr om, 1970; Kloeden & Platen, 1992), the Itô interpretation is adapted here.”
Non-exponential stability and decay rates in nonlinear stochastic difference equations with unbounded noise (2006, unknown): “The corresponding property is called “A-stability” and it has been addressed in the stochastic context in [8], [ 11 ], [19].”
Probabilistic Characterization of Thermostatically Controlled Loads to Model the Impact of Demand Response Programs (2011, methodology): “1) Simulation of a Single Individual Load: The first step involves the implementation of an Euler-Maruyama discretization scheme [ 32 ] in order to solve (2).”
The Milstein Scheme for Stochastic Delay Differential Equations Without Using Anticipative Calculus (2012, methodology): “The iterative repetition of this idea underlies the systematic derivation of stochastic Taylor expansions and numerical schemes of arbitrarily high strong and weak orders, as expounded in Kloeden and Platen [ 9 ], see also Milstein [ 12 ].”
Exact Solutions of Stochastic Differential Equations: Gompertz, Generalized Logistic and Revised Exponential (2010, methodology): “A systematic method for reducing a non-linear SDE to a linear one was due to Kloeden and Platen (1999) and Kloeden et al. (1992, 2003).”
The partially truncated Euler–Maruyama method and its stability and boundedness (2017, unknown): “, [5, 14]) dx(t) = (ax(t)− bx(3)(t))dt+ cx(t)dB(t), (1.”
On Unscented Kalman Filtering for State Estimation of Continuous-Time Nonlinear Systems (2007, methodology): “The simulation was performed over time period of 5 s using the Euler-Maruyama scheme [ 33 ] and with time steps of .”