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A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, [1] resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices , [ 2 ] random ...
Supersymmetric theory of stochastic dynamics or stochastics (STS) is an exact theory of stochastic (partial) differential equations (SDEs), the class of mathematical models with the widest applicability covering, in particular, all continuous time dynamical systems, with and without noise.
In Itô calculus, the Euler–Maruyama method (also simply called the Euler method) is a method for the approximate numerical solution of a stochastic differential equation (SDE). It is an extension of the Euler method for ordinary differential equations to stochastic differential equations named after Leonhard Euler and Gisiro Maruyama. The ...
A stochastic process S t is said to follow a GBM if it satisfies the following stochastic differential equation (SDE): = + where is a Wiener process or Brownian motion, and ('the percentage drift') and ('the percentage volatility') are constants.
A stochastic differential equation (SDE) is an equation in which the unknown quantity is a stochastic process and the equation involves some known stochastic processes, for example, the Wiener process in the case of diffusion equations. A stochastic partial differential equation (SPDE) is an equation that generalizes SDEs to include space-time ...
In mathematics of stochastic systems, the Runge–Kutta method is a technique for the approximate numerical solution of a stochastic differential equation. It is a generalisation of the Runge–Kutta method for ordinary differential equations to stochastic differential equations (SDEs). Importantly, the method does not involve knowing ...
Stochastic mechanics is a framework for describing the dynamics of particles that are subjected to an intrinsic random processes as well as various external forces. The framework provides a derivation of the diffusion equations associated to these stochastic particles.
The model specifies that the instantaneous interest rate follows the stochastic differential equation: = + where W t is a Wiener process under the risk neutral framework modelling the random market risk factor, in that it models the continuous inflow of randomness into the system.
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