Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance

6Stochastic integrals

6.1 Informal definition of the Itô and Stratonovich integrals

The Black–Scholes model (3.4) is a particular case of a stochastic differential equation, but we are going to study in this book the more general case of stochastic differential equations (SDEs) in a time interval () of the form

(6.1)

where and are real functions with domain and (initial condition) is a r.v. independent of the Wiener process . The initial condition can, in particular, be deterministic, i.e. assume a constant real value (in which case we may say that the r.v. is degenerate and assumes the ...