Displaying similar documents to “Renormalization group of and convergence to the LISDLG process”

Simulation and approximation of Lévy-driven stochastic differential equations

Nicolas Fournier (2012)

ESAIM: Probability and Statistics

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We consider the approximate Euler scheme for Lévy-driven stochastic differential equations. We study the rate of convergence in law of the paths. We show that when approximating the small jumps by Gaussian variables, the convergence is much faster than when simply neglecting them. For example, when the Lévy measure of the driving process behaves like ||d near , for some (1,2), we obtain an error of order 1/√ with a computational cost of order . For a similar error when...

Simulation and approximation of Lévy-driven stochastic differential equations

Nicolas Fournier (2011)

ESAIM: Probability and Statistics

Similarity:

We consider the approximate Euler scheme for Lévy-driven stochastic differential equations. We study the rate of convergence in law of the paths. We show that when approximating the small jumps by Gaussian variables, the convergence is much faster than when simply neglecting them. For example, when the Lévy measure of the driving process behaves like ||d near , for some ∈ (1,2), we obtain an error of order 1/√ with a computational cost of order . For a similar error when neglecting...

Linear diffusion with stationary switching regime

Xavier Guyon, Serge Iovleff, Jian-Feng Yao (2010)

ESAIM: Probability and Statistics

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Let be a Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic process : ddd. We establish that under the condition with the stationary distribution of the regime process , the diffusion is ergodic. We also consider conditions for the existence of moments for the invariant law of when is a Markov jump process having a finite number of states. Using results on random difference equations on one hand and the fact that conditionally to , is Gaussian on the other...