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  2. Lawrence C. Evans - Wikipedia

    en.wikipedia.org/wiki/Lawrence_C._Evans

    Lawrence Craig Evans (born November 1, 1949) is an American mathematician and Professor of Mathematics at the University of California, Berkeley.. His research is in the field of nonlinear partial differential equations, primarily elliptic equations.

  3. Stochastic differential equation - Wikipedia

    en.wikipedia.org/wiki/Stochastic_differential...

    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 ...

  4. Geometric Brownian motion - Wikipedia

    en.wikipedia.org/wiki/Geometric_Brownian_motion

    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.

  5. Stochastic processes and boundary value problems - Wikipedia

    en.wikipedia.org/wiki/Stochastic_processes_and...

    Let be a domain (an open and connected set) in .Let be the Laplace operator, let be a bounded function on the boundary, and consider the problem: {() =, = (),It can be shown that if a solution exists, then () is the expected value of () at the (random) first exit point from for a canonical Brownian motion starting at .

  6. Stochastic analysis on manifolds - Wikipedia

    en.wikipedia.org/wiki/Stochastic_analysis_on...

    In mathematics, stochastic analysis on manifolds or stochastic differential geometry is the study of stochastic analysis over smooth manifolds. It is therefore a synthesis of stochastic analysis (the extension of calculus to stochastic processes ) and of differential geometry .

  7. Deep backward stochastic differential equation method

    en.wikipedia.org/wiki/Deep_backward_stochastic...

    Evans, Lawrence C (2013). An Introduction to Stochastic Differential Equations American Mathematical Society. Higham., Desmond J. (January 2001). "An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations". SIAM Review. 43 (3): 525– 546. Bibcode:2001SIAMR..43..525H. CiteSeerX 10.1.1.137.6375.

  8. Obstacle problem - Wikipedia

    en.wikipedia.org/wiki/Obstacle_problem

    Evans, Lawrence, An Introduction to Stochastic Differential Equations (PDF), p. 130. A set of lecture notes surveying "without too many precise details, the basic theory of probability, random differential equations and some applications", as the author himself states.

  9. Euler–Maruyama method - Wikipedia

    en.wikipedia.org/wiki/Euler–Maruyama_method

    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 ...

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