Stochastic

by Wei Liu (Author), Michael Röckner (Author)
A concise and as self-contained as possible introduction to the ‘variational approach’ of SPDEs
Provides a very detailed introduction to stochastic integration on Hilbert spaces
Includes a complete proof of the finite-dimensional case using the Euler approximation

Authors: Le Gall, Jean-François
Provides a concise and rigorous presentation of stochastic integration and stochastic calculus for continuous semimartingales
Presents major applications of stochastic calculus to Brownian motion and related stochastic processes
Includes important aspects of Markov processes with applications to stochastic differential equations and to connections with partial differential equations

In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking.

In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems.

In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems.