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A note on Newton's method for system of stochastic differential equations
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Reza Habibi
Published/Copyright:
November 29, 2012
Abstract.
Kawabata and Yamada (1991) proposed an implicit formulation for Newton's method for an univariate stochastic differential equation (SDEs). Amano (2009) used the linearized equation technique and proposed explicit formulation for the Newton scheme. In this note, we extend the Newton method for univariate SDEs to the multivariate cases. The error analysis is given and some examples are proposed. Results show that the method works well.
Keywords: Integrated processes; multivariate stochastic
differential equations; Newton's method; second order diffusion process
Received: 2011-03-02
Accepted: 2012-08-03
Published Online: 2012-11-29
Published in Print: 2012-12-01
© 2012 by Walter de Gruyter Berlin Boston
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- Masthead
- A note on Newton's method for system of stochastic differential equations
- Quantization based recursive importance sampling
- Dynamical system generated by algebraic method and low discrepancy sequences
- Improving the Monte Carlo estimation of boundary crossing probabilities by control variables
Keywords for this article
Integrated processes;
multivariate stochastic
differential equations;
Newton's method;
second order diffusion process
Articles in the same Issue
- Masthead
- A note on Newton's method for system of stochastic differential equations
- Quantization based recursive importance sampling
- Dynamical system generated by algebraic method and low discrepancy sequences
- Improving the Monte Carlo estimation of boundary crossing probabilities by control variables
