## 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.

(

**2740**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.

(

**1793**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.

(

**3244**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.

(

**2992**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.

(

**3260**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.

(

**4536**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.

(

**5176**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.

(

**4728**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.

(

**4699**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.

(

**7123**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.

(

**6229**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.

(

**7420**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.

(

**8830**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.

(

**9663**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.

(

**10227**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.

(

**11100**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.

(

**15630**views)