Approximate controllability of stochastic differential systems driven by a Lévy process

In this paper, we are concerned with the approximate controllability of stochastic differential systems driven by Teugels martingales associated with a Lévy process. We derive the approximate controllability with the coefficients in the system satisfying some non-Lipschitz conditions, which include classic Lipschitz conditions as special cases. The desired result is established by means of standard Picard’s iteration.

[1]  Zhen Wu,et al.  Stochastic differential equations and stochastic linear quadratic optimal control problem with Lévy processes , 2009, J. Syst. Sci. Complex..

[2]  Rathinasamy Sakthivel,et al.  Complete Controllability of Stochastic Evolution Equations with Jumps , 2011 .

[3]  Nazim I. Mahmudov.  Controllability of linear stochastic systems , 2001, IEEE Trans. Autom. Control..

[4]  R. Wolpert.  Lévy Processes , 2000 .

[5]  Nazim I. Mahmudov,et al.  Approximate controllability of evolution systems with nonlocal conditions , 2008 .

[6]  C. Knoche.  Mild solutions of SPDE's driven by Poisson noise in infinite dimensions and their dependence on initial conditions , 2005 .

[7]  D. Nualart,et al.  Backward stochastic differential equations and Feynman-Kac formula for Levy processes, with applications in finance , 2001 .

[8]  Nazim I. Mahmudov,et al.  Approximate Controllability of Semilinear Deterministic and Stochastic Evolution Equations in Abstract Spaces , 2003, SIAM J. Control. Optim..

[9]  I. Bihari.  A generalization of a lemma of bellman and its application to uniqueness problems of differential equations , 1956 .

[10]  Jerzy Klamka,et al.  Constrained controllability of semilinear systems with delays , 2009 .

[11]  D. Nualart,et al.  Chaotic and predictable representation for L'evy Processes , 2000 .

[12]  йордан Дуйгев.  О простых идеалах первой степени , 1956 .

[13]  Jorge A. León,et al.  On Lévy processes, Malliavin calculus and market models with jumps , 2002, Finance Stochastics.

[14]  Hong Xing Zhou,et al.  Approximate Controllability for a Class of Semilinear Abstract Equations , 1983 .

[15]  Nazim I. Mahmudov,et al.  On Concepts of Controllability for Deterministic and Stochastic Systems , 1999 .

[16]  佐藤 健一.  Lévy processes and infinitely divisible distributions , 2013 .