Kind assist me solve the question below

Let S, be a geometric Brownian motion process defined by the equation S, = exp(/t+OW,), where W, is a standard Brownian motion and # and o are constants. (1) Write down the stochastic differential equation satisfied by X", = log, S,. [1] (ii) By applying Ito's Lemma, or otherwise, write down the stochastic differential equation satisfied by S,. [3] (iii) The price of a share follows a geometric Brownian motion with / =0.06 and (T= 0).25 (both expressed in annual units). Find the probability that, over a given one-year period, the share price will fall. 13] [Total ?]The following two time series equations have been suggested for modelling I , the annual force of inflation, and Y, , the equity dividend yield on an equity index: I = 0.03 1 0.4(1,_1 0.03) 1 0.012, In Y = (In D.03 +1.2/, )+0.5, In Y_, -(In0.03+1.21,_,) +0.047, where 7, and 7 are uncorrelated N (0,1) variables (i) Explain the key features of the Y equation, commenting on its plausibility for the purpose of modelling the equity dividend yield. [5] (ii) Transform the two equations into their VARMA form. [4] [Total 9]