Abstract
We give large deviation estimates for a convolution semigroup, which is not Markovian and of Lévy type, of big order.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J. Chazarain, A. Piriou, Introduction a la théorie des équations aux dérivées partielles linéaires (Gauthier-Villars, 1981)
E.B. Davies, Bull. Lond. Math. Soc. 29, 513–546 (1997)
J. Dieudonné, Eléments d’Analyse VII (Gauthiers-Villars, 1977)
M.V. Fedoriuk, V.P. Maslov, Semiclassical Approximation in Quantum Mechanics (Reidel, New York, 1981)
M.J. Freidlin, A.D. Wentzel, Random Perturbations of Dynamical Systems (Springer, New York, 1984)
L. Hoermander, The Analysis of Linear Partial Operators III (Springer, Berlin, 1984)
L. Hoermander, The Analysis of Linear Partial Operators IV (Springer, Berlin, 1984)
N. Jacob, Pseudo-differential Operators and Markov Processes. I. Fourier Analysis and Semigroups (Imperial College Press, London, 2001)
N. Jacob, Pseudo-differential Operators and Markov Processes. II. Generators and Their Potential Theory (Imperial College Press, London, 2003)
N. Jacob, Pseudo-differential Operators and Markov Processes. III. Markov Processes and Their Applications (Imperial College Press, London, 2005)
R. Léandre, Extension du théoreme de Hörmander a divers processus de sauts. PHD thesis, Université de Besançon, France (1984)
R. Léandre, Itô-Stratonovitch formula for a four order operator on a Torus. Acta. Physica Debrecin 42, 133–138 (2008). Non-Euclidean Geometry and Its Applications
R. Léandre, Itô-Stratonovitch formula for the Schroedinger equation associated to a big order operator on a Torus. Physica Scripta 136 (2009). Article 014028. Fractional Order Differentiation
R. Léandre, Itô-Stratonovitch formula for the wave equation on a Torus, in Computations of Stochastic Systems. Trans. Comput. Sci. VII. Lecture Notes in Computer Science, vol. 5890 (Springer, 2009), pp. 68–75
R. Léandre, Itô formula for an integro-differential operator without a stochastic process, in ISAAC 2009, Honolulu (World Scientific, 2010), pp. 225–231
R. Léandre, Stochastic analysis without probability: study of some basic tools. J. Pseudo-Differ. Oper. Appl. 1, 389–410 (2010)
R. Léandre, A generalized Fock space associated to a Bilaplacian, in 2011 World Congress Engineering Technology (C.D. I.E.E.E., 2011), pp. 68–72
R. Léandre, Long time behaviour on a path group of the heat semi-group associated to a Bilaplacian. Symmetry 3, 72–83 (2011). Symmetry Measures on Complex Networks
R. Léandre, A path-integral Approach to the Cameron-Martin-Maruyama-Girsanov formula associated to a Bilaplacian. J. Funct. Spaces Appl. (2012). Article 458738. Integral and Differential Systems in Function Spaces
R. Léandre, An Itô formula for an accretive operator. Axioms 1, 4–8 (2012). Axioms: Feature Papers
R. Léandre, A Girsanov formula associated to a big order pseudo-differential operators. Cubo Math. J. 15, 113–119 (2013). Festchrift in Honour of G. N’Guérékata
R. Léandre, The stochastic flow theorem for an operator of order four, in Geometry of Science Information 2013. Lecture Notes in Computer Science, vol. 8085 (Springer, Heidelberg, 2013), pp. 497–502
R. Léandre, Wentzel-Freidlin estimates for an operator of order four, in 2014 International Conference on Computational Science and Computational Intelligence (IEEE Computer Society, Los Alamitos, 2014), pp. 360–364
R. Léandre, Stochastic analysis for a non-Markovian generator: an introduction. Russ. J. Math. Phys. 22, 39–52 (2015)
R. Léandre, The Itô-Stratonovitch formula for an operator of order four. Festchrift in Honour ov A. Mukharjea, P. Feinsilver, S. Mohammed, Contemporary Mathematics (To appear)
R. Léandre, Large deviation estimates for a non-Markovian Lévy generator of big order. J. Phys.: Conf. Ser. 633 (2015), Article 12085. 4th International Conference on Mathematical Modeling in Physical Sciences
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Léandre, R. (2017). A Class of Non-Markovian Pseudo-differential Operators of Lévy Type. In: Wong, M., Zhu, H. (eds) Pseudo-Differential Operators: Groups, Geometry and Applications. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-47512-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-47512-7_8
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-47511-0
Online ISBN: 978-3-319-47512-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)