Now I would like to define the integrals of the following type, the integrals Xt dHt from a to b. Here, H is some stochastic process. Namely, I will consider H of t from the class of Ito processes. Well, this means that this process can be represented in the following form, H of t is equal to H0 plus integral from zero to t bs ds plus integral from zero to t sigma s dWs. W is a Brownian motion. And here, we assume that there is some filtration behind this integral. So, F of t is a filtration. Bs and sigma s are two processes which are adapted to this filtration. So, processes adapted to Ft. Brownian motion is Ft Brownian motion. And H0 is a random variable which is measurable with respect to F0. So, here, Ht is a process of this type, and X is some process adapted to the same filtration. And if the process Xt is such that the integral from a to b absolute value of X as bs plus Xs squared sigma s squared, ds is finate, if X is such that this condition is fulfilled, then we define the integral from a to b Xt dHt is equal to the integral from a to b bs Xsds plus integral from a to b sigma s XsdWs. Know that here, we'll have two integrals of the type which we considered before, namely: the first integral is the first type and take s as the basic process and integrate it with respect to ds. And the second integral was also considered before because here, we have an integral with respect to Brownian motion. This is the first and the third type of the integrals which were considered before. This is just a definition, nothing more. And if the process H of t kind of represents this form, one can also use an alternative notation for this class of processes, namely: one can write that the process Ht is formed in the following ways. So, one can write dHt is equal to btdt plus sigma tdt. This is just another notation of the same object, nothing more. By definition, this Stochastic differential equation Stochastic representation is the same as this Stochastic integral, nothing more. The following theorem plays essential role in the theory of integrals of this type. Let me assume that H of t is an Ito process, and F is some function of two arguments t and x, which is twice continuously differential. Then, the following statement holds. The process F (t, H of t) is itself an Ito process. And what is very important is that it is equal to F(0, H0) plus the derivative of the function F with respect to the first variable. I will denote it by F1 prime. At the moment, S, H of s. And I will integrate this function with respect to ds, integral from zero to t. Plus integral from zero to t, is the first derivative of the function F with respect to the second argument. F2 prime s, H of s, dH of s, this is just an integral of this type, an integral with respect to the Ito process. But this is not all. Plus, and here I should write, one half integral from zero to t. And now I should take the second derivative of the function F with respect to the second argument. So, F22 to prime is at s, H of s multiplied by the coefficient which is here. So this sigma s is the power two. So, sigma s squared. And now I should write ds. This formula is known as the Ito formula. At the first glance, it looks like a magic. So it's a very complicated thing which is not clear how to use. But in the next subsection, I will show you an example how this formula helps to calculate the basic integrals of different types.