sde

: ''For the video display issue known as SDE, see Screen door effect.''A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, thus resulting in a solution which is itself a stochastic process.

Use in physics - For example a general, coupled set of first-order SDEs (note that there are standard techniques for transforming a higher-order equation into several coupled first-order equations by introducing new unknowns) is often written in the form::$\backslash dot\; \_i\; =\; \backslash frac\; =\; f\_i(\backslash mathbf\; )\; +\; \backslash sum\_\; ^ng\_i^m(\backslash mathbf\; !)\backslash eta\_m(t),\backslash ,$wher e? $\backslash mathbf\; =\backslash$ is the set of unknowns, the $f\_i$ and $g\_i$ are arbitrary functions and the !$\backslash eta\_mg\_i$ are constants, the system is said to be subject to additive noise, otherwise it is said to be subject to multiplicative noise.The main method of solution is by use of the Fokker-Planck equation, which provides a deterministic equation satisfied by the time dependant probability density. Alternatively numerical solutions can be obtained by Monte Carlo MethodMonte Carlo simulation. Other techniques, such as path integral formulationpath integration have also been used, drawing on the analogy between statistical physics and quantum mechanics (for example the Fokker-Planck equation can be transformed into the Schrodinger equation by rescaling a few variables).

Use in probability and financial mathematics - The notation used in the context of financial mathematics as well as in probability theory is slightly different. A typical equation is of the form:$dX\_t\; =\; \backslash mu(X\_t,t)\backslash ,\; dt\; +\; \backslash sigma(X\_t,t)\backslash ,\; dB\_t\backslash ,.$This equation should be interpreted as a slightly colloquial way of expressing the corresponding integral equation:$X\_t\; =\; \backslash int\; \backslash mu(X\_t,t)\; dt\; +\; \backslash int\; \backslash sigma(X\_t,t)\backslash ,\; dB\_t.$The equation above characterises the behavior of the continuous time stochastic process !''X''_{''t''''t''(\Omega,F,P)\,< /math>.? A weak solution consists of a probability space and a process that satisfies the integral equation, while a strong solution is a process that satisfies the equation and is defined on a given probability space.An important example is the equation for geometric Brownian motion:$dX\_t\; =\; \backslash mu\; X\_t\backslash ,\; dt\; +\; \backslash sigma\; X\_t\backslash ,\; dB\_t.$which is the equation for the dynamics of the price of a stock in the Black Scholes options pricing model of financial !mathematics.Category:Different ial? equationsCategory:Stochastic processes DEBUG REDIRECT (stochastic differential equation)}

ConneCT
Official website for the State of Connecticut, providing information on the agencies, organizations, departments and all other aspects of state government.
http://www.state.ct.us/

New Mexico State Department of Education
Official site.
http://sde.state.nm.us/

Oklahoma State Department of Education
Education news and events for Oklahoma Public Schools.
http://sde.state.ok.us/

SDE - Staff Development for Educators
Seminars, conferences, customized training services, and books for pre-kindergarten to grade 12 teachers. Lists conference schedules by topic and location, registration form, and graduate credit information by state.
http://www.sde.com/