Stochastic Calculus for Finance I: Binomial asset pricing model and Stochastic Calculus for Finance II: tochastic Calculus for Finance II: Continuous-Time Models. These two books are very good if you want to apply the theory to price derivatives. Stochastic Differential Equations: An Introduction with Applications Bernt Oksanda.
This book provides a lively and accessible introduction to the numerical solution of stochastic differential equations with the aim of making this subject available to the widest possible readership.
Explore related questions probability probability-theory stochastic-processes stochastic-calculus stochastic-differential-equations See similar questions with these tags.
This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its ...
Stochastic Volterra integral equations provide a powerful framework for modelling systems in which memory effects and hereditary properties play a central role. These equations extend the classical ...
A stochastic process is a colection of random variables defined on the same probability space. Please explain further what parts of this definition are escaping you.
What's the difference between stochastic and random? There is an anecdote about the notion of stochastic processes. They say that when Khinchin wrote his seminal paper "Correlation theory for stationary stochastic processes", this did not go well with Soviet authorities. The reason is that the notion of random process used by Khinchin contradicted dialectical materialism. In diamat, all ...
An intuitive logical consequence of that interpretation is that the "law" or "underlying mechanism" that determines the stochastic process must be time-invariant. On the other hand, my understanding of the time homogeneous condition is that it explicitly states the time-invariance of the "law" or "underlying mechanism" of the stochastic process.