Stochastic Calculus

e-books in Stochastic Calculus category

Stochastic Differential Equations: Models and Numerics
by Anders Szepessy, et al. - KTH , 2010
The goal of this course is to give useful understanding for solving problems formulated by stochastic differential equations models in science, engineering and finance. Typically, these problems require numerical methods to obtain a solution.
(7974 views)

Lectures on Singular Stochastic PDEs
by M. Gubinelli, N. Perkowski - arXiv , 2015
The aim is to introduce the basic problems of non-linear PDEs with stochastic and irregular terms. We explain how it is possible to handle them using two main techniques: the notion of energy solutions and that of paracontrolled distributions.
(6724 views)

Introduction to Stochastic Processes
by Gordan Žitković - The University of Texas at Austin , 2010
Contents: Probability review; Mathematica in 15 minutes; Stochastic Processes; Simple random walk; Generating functions; Random walks - advanced methods; Branching processes; Markov Chains; The 'Stochastics' package; Classification of States; etc.
(8019 views)

Applied Stochastic Processes in Science and Engineering
by Matt Scott - University of Waterloo , 2013
This book is designed as an introduction to the ideas and methods used to formulate mathematical models of physical processes in terms of random functions. A senior undergraduate course offered to students with a suitably mathematical background.
(8272 views)

Advanced Stochastic Processes
by Jan A. Van Casteren - Bookboon , 2013
In this book, which is basically self-contained, the following topics are treated thoroughly: Brownian motion as a Gaussian process, Brownian motion as a Markov process, Brownian motion as a martingale, Markov chains, renewal theory, etc.
(8033 views)

Lectures on Stochastic Flows and Applications
by H. Kunita - Tata Institute Of Fundamental Research , 1986
The author presents basic properties of stochastic flows, specially of Brownian flows and their relations with local characteristics and with stochastic differential equations. Various limit theorems for stochastic flows are presented.
(9090 views)

Lectures on Stochastic Differential Equations and Malliavin Calculus
by S. Watanabe - Tata Institute of Fundamental Research , 1984
The author's main purpose in these lectures was to study solutions of stochastic differential equations as Wiener functionals and apply to them some infinite dimensional functional analysis. This idea was due to P. Malliavin.
(10315 views)

Stochastic Processes
by Leif Mejlbro - BookBoon , 2012
In this book you will find the basic stochastic processes mathematics that is needed by engineers and university students. Topics such as elementary probability calculus, density functions and stochastic processes are illustrated.
(10348 views)

Lectures on Topics in Stochastic Differential Equations
by Daniel W. Stroock - Tata Institute of Fundamental Research , 1982
The author's purpose in these lectures was to provide some insight into the properties of solutions to stochastic differential equations. In order to read these notes, one need only know the basic Ito theory of stochastic integrals.
(10074 views)

Lectures on Stochastic Processes
by K. Ito - Tata Institute of Fundamental Research , 1960
The book discusses the elementary parts of Stochastic Processes from the view point of Markov Processes. Topics: Markov Processes; Srong Markov Processes; Multi-dimensional Brownian Motion; Additive Processes; Stochastic Differential Equations; etc.
(12618 views)

Probability Theory and Stochastic Processes with Applications
by Oliver Knill - Overseas Press , 2009
This text covers material of a basic probability course, discrete stochastic processes including Martingale theory, continuous time stochastic processes like Brownian motion and stochastic differential equations, estimation theory, and more.
(12305 views)

Synchronization and Linearity: An Algebra for Discrete Event Systems
by F. Baccelli, G. Cohen, G. J. Olsder, J. Quadrat - John Wiley & Sons , 1993
Presents new modelling and analysis techniques for the description of discrete event dynamic systems. Created within the text is a calculus which allows the derivation of analytical tools for computing the time behavior of this type of system.
(14070 views)

Nonlinear Parameter Estimation: An Integrated System in Basic
by John C. Nash - Marcel Dekker Inc , 1995
This book and software collection is intended to help scientists, engineers and statisticians in their work. We have collected various software tools for nonlinear parameter estimation, along with representative example problems.
(15112 views)

Stochastic Analysis - Notes
by I. F. Wilde , 2009
A gentle introduction to the mathematics of Stochastic Analysis. From the table of contents: Introduction; Conditional expectation; Martingales; Stochastic integration - informally; Wiener process; Ito's formula; Bibliography.
(15300 views)

Stochastic Calculus
by Alan Bain , 2008
An informal introduction to Stochastic Calculus, and especially to the Ito integral and some of its applications. The text concentrates on the parts of the course which the author found hard, there is little or no comment on more standard matters.
(16381 views)

Reversibility and Stochastic Networks
by F.P. Kelly - John Wiley and Sons Ltd , 1979
The book on vector stochastic processes in equilibrium or stochastic networks, with wide range of applications. It covers the concept of reversibility, the output from a queue, and the epolymerization process quilibrium distribution.
(17281 views)

Markov Chains and Stochastic Stability
by S.P. Meyn, R.L. Tweedie - Springer , 2005
The book on the theory of general state space Markov chains, and its application to time series analysis, operations research and systems and control theory. An advanced graduate text and a monograph treating the stability of Markov chains.
(22324 views)