Free energy adopted stochastic optimization protein folding

Optimal structure of proteins is described by linear stochastic differential equation with mean decrease of free energy and volatility. Structure determining strategy is given by a twin of stochastic variables for which empirical conditions are not postulated. Optimal structure determination will be deformed to be adoptive to trading strategy employing martingale property where stochastic integral w.r.t. analytical solution of stochastic differential equation will be employed. 1. Stochastic Optimization . 1.1. Stochastic Differential Equation. Let us start from heat equation (1.1) ∂u ∂t = 1 2 ∂u ∂2x2 , the solution is given by (1.2) u = 1 √ 2πt e− u2 2t , and corresponding stochastic differential equation is (1.3) dut = dBt, where Bt denotes Brownian motion. In case there is a drift term we have (1.4) dut = −cdt+ dBt, whose solution is (1.5) u = 1 √ 2πt e− (u−ct)2 2t , where c is a velocity. Let us modify the last equation to be (1.6) xt = cdt+ √ αdBt, where α is volatility. This equation can be integrated to be