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Stochastic integrals and SDE driven by nonlinear lévy noise. / Kolokoltsov, Vassili N.

Stochastic Analysis 2010. Springer Nature, 2011. p. 227-242.

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Harvard

Kolokoltsov, VN 2011, Stochastic integrals and SDE driven by nonlinear lévy noise. in Stochastic Analysis 2010. Springer Nature, pp. 227-242. https://doi.org/10.1007/978-3-642-15358-7_11

APA

Kolokoltsov, V. N. (2011). Stochastic integrals and SDE driven by nonlinear lévy noise. In Stochastic Analysis 2010 (pp. 227-242). Springer Nature. https://doi.org/10.1007/978-3-642-15358-7_11

Vancouver

Kolokoltsov VN. Stochastic integrals and SDE driven by nonlinear lévy noise. In Stochastic Analysis 2010. Springer Nature. 2011. p. 227-242 https://doi.org/10.1007/978-3-642-15358-7_11

Author

Kolokoltsov, Vassili N. / Stochastic integrals and SDE driven by nonlinear lévy noise. Stochastic Analysis 2010. Springer Nature, 2011. pp. 227-242

BibTeX

@inbook{056e98a44b9e407eb25d5c19ea1170e1,
title = "Stochastic integrals and SDE driven by nonlinear l{\'e}vy noise",
abstract = "We develop the theory of SDE driven by nonlinear L{\'e}vy noise, aiming at applications to Markov processes. It is shown that a conditionally positive integro-differential operator (of the L{\'e}vy-Khintchine type) with variable coefficients (diffusion, drift and L{\'e}vy measure) depending Lipschitz continuously on its parameters generates a Markov semigroup, where the measures are metricized by the Wasserstein-Kantorovich metrics Wp . The analysis of SDE driven by nonlinear L{\'e}vy noise was initiated by the author in (Kolokoltsov, Probability Theory Related Fields, DOI: 10.1007/s00440-010-0293-8, 2009) (inspired partially by Carmona and Nualart, Nonlinear Stochastic Integrators, Equations and Flows, Stochatic Monographs, v. 6, Gordon and Breach, 1990), see also (Kolokoltsov, Nonlinear Markov Processes and Kinetic Equations, Monograph. To appear in CUP, 2010). Here, we suggest an alternative (seemingly more straightforward) approach based on the path-wise interpretation of these integrals as nonhomogeneous L{\'e}vy processes. Moreover, we are working with more general Wp -distances rather than with W2.",
keywords = "Markov processes, Nonlinear integrators, Pseudo-differential operators, SDE driven by L{\'e}vy noise, Wasserstein- Kantorovich metric",
author = "Kolokoltsov, {Vassili N.}",
year = "2011",
doi = "10.1007/978-3-642-15358-7_11",
language = "English",
isbn = "9783642153570",
pages = "227--242",
booktitle = "Stochastic Analysis 2010",
publisher = "Springer Nature",
address = "Germany",

}

RIS

TY - CHAP

T1 - Stochastic integrals and SDE driven by nonlinear lévy noise

AU - Kolokoltsov, Vassili N.

PY - 2011

Y1 - 2011

N2 - We develop the theory of SDE driven by nonlinear Lévy noise, aiming at applications to Markov processes. It is shown that a conditionally positive integro-differential operator (of the Lévy-Khintchine type) with variable coefficients (diffusion, drift and Lévy measure) depending Lipschitz continuously on its parameters generates a Markov semigroup, where the measures are metricized by the Wasserstein-Kantorovich metrics Wp . The analysis of SDE driven by nonlinear Lévy noise was initiated by the author in (Kolokoltsov, Probability Theory Related Fields, DOI: 10.1007/s00440-010-0293-8, 2009) (inspired partially by Carmona and Nualart, Nonlinear Stochastic Integrators, Equations and Flows, Stochatic Monographs, v. 6, Gordon and Breach, 1990), see also (Kolokoltsov, Nonlinear Markov Processes and Kinetic Equations, Monograph. To appear in CUP, 2010). Here, we suggest an alternative (seemingly more straightforward) approach based on the path-wise interpretation of these integrals as nonhomogeneous Lévy processes. Moreover, we are working with more general Wp -distances rather than with W2.

AB - We develop the theory of SDE driven by nonlinear Lévy noise, aiming at applications to Markov processes. It is shown that a conditionally positive integro-differential operator (of the Lévy-Khintchine type) with variable coefficients (diffusion, drift and Lévy measure) depending Lipschitz continuously on its parameters generates a Markov semigroup, where the measures are metricized by the Wasserstein-Kantorovich metrics Wp . The analysis of SDE driven by nonlinear Lévy noise was initiated by the author in (Kolokoltsov, Probability Theory Related Fields, DOI: 10.1007/s00440-010-0293-8, 2009) (inspired partially by Carmona and Nualart, Nonlinear Stochastic Integrators, Equations and Flows, Stochatic Monographs, v. 6, Gordon and Breach, 1990), see also (Kolokoltsov, Nonlinear Markov Processes and Kinetic Equations, Monograph. To appear in CUP, 2010). Here, we suggest an alternative (seemingly more straightforward) approach based on the path-wise interpretation of these integrals as nonhomogeneous Lévy processes. Moreover, we are working with more general Wp -distances rather than with W2.

KW - Markov processes

KW - Nonlinear integrators

KW - Pseudo-differential operators

KW - SDE driven by Lévy noise

KW - Wasserstein- Kantorovich metric

UR - http://www.scopus.com/inward/record.url?scp=84873367463&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-15358-7_11

DO - 10.1007/978-3-642-15358-7_11

M3 - Chapter

AN - SCOPUS:84873367463

SN - 9783642153570

SP - 227

EP - 242

BT - Stochastic Analysis 2010

PB - Springer Nature

ER -

ID: 86493419