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Status:
Available4.5
21 reviews
ISBN 10: 3110278898
ISBN 13: 9783110278897
Author: Rene L. Schilling, Lothar Partzsch
Stochastic processes occur in a large number of fields in sciences and engineering, so they need to be understood by applied mathematicians, engineers and scientists alike. This work is ideal for a first course introducing the reader gently to the subject matter of stochastic processes. It uses Brownian motion since this is a stochastic process which is central to many applications and which allows for a treatment without too many technicalities. All chapters are modular and are written in a style where the lecturer can "pick and mix" topics. A "dependence chart" will guide the reader when arrange her/his own digest of material.
Robert Brown’s new thing
Brownian motion as a Gaussian process
Constructions of Brownian motion
The canonical model
Brownian motion as a martingale
Brownian motion as a Markov process
Brownian motion and transition semigroups
The PDE connection
The variation of Brownian paths
Regularity of Brownian paths
The growth of Brownian paths
Strassen’s Functional Law of the Iterated Logarithm
Skorokhod representation
Stochastic integrals: L2-Theory
Stochastic integrals: beyond L2T
Itô’s formula
Applications of Itô’s formula
Stochastic differential equations
On diffusions
Simulation of Brownian motion
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Tags: Rene L Schilling, Lothar Partzsch, Brownian Motion, Introduction, Stochastic Process
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