Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations

• Autores: A.E. Tyukov, V.N. Kolokol'tsov, René L. Schilling
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 20, Nº 2, 2004, págs. 333-380
• Idioma: inglés
• DOI: 10.4171/rmi/392
• Títulos paralelos:
  • Estimaciones para integrales estocásticas múltiples y ecuaciones de Hamilton-Jacobi estocásticas.
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• Resumen

  • We study stochastic Hamilton-Jacobi-Bellman equations and the corresponding Hamiltonian systems driven by jump-type Lévy processes. The main objective of the present papel is to show existence, uniqueness and a (locally in time) diffeomorphism property of the solution: the solution trajectory of the system is a diffeomorphism as a function of the initial momentum. This result enables us to implement a stochastic version of the classical method of characteristics for the Hamilton-Jacobi equations. An -in itself interesting- auxiliary result are pointwise a.s. estimates for iterated stochastic integrals driven by a vector of not necessarily independent jump-type semimartingales.