Results 271 to 280 of about 561,284 (332)

Stochastic Differential Equations

2014
Stochastic differential equations describe the time evolution of certain continuous n-dimensional Markov processes. In contrast with classical differential equations, in addition to the derivative of the function, there is a term that describes the random fluctuations that are coded as an Ito integral with respect to a Brownian motion. Depending on how
Etienne Pardoux, Aurel Răşcanu
  +10 more sources

Stochastic Differential Equations [PDF]

, 1990
A diffusion can be thought of as a strong Markov process (in ℝn) with continuous paths. Before the development of Ito’s theory of stochastic integration for Brownian motion, the primary method of studying diffusions was to study their transition semigroups.
R. J. Williams, K. L. Chung
  +6 more sources

The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations

SIAM Journal on Scientific Computing, 2002
We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of ...
Dongbin Xiu, G. Karniadakis
semanticscholar   +1 more source

Stochastic differential equations : an introduction with applications

, 1987
Some Mathematical Preliminaries.- Ito Integrals.- The Ito Formula and the Martingale Representation Theorem.- Stochastic Differential Equations.- The Filtering Problem.- Diffusions: Basic Properties.- Other Topics in Diffusion Theory.- Applications to ...
B. Øksendal
semanticscholar   +1 more source

Stochastic Partial Differential Equations

Computer Vision, 2014
Annika Lang
openaire   +3 more sources

Stochastic Differential Equations [PDF]

, 1988
We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of ...
Steven E. Shreve, Ioannis Karatzas
openaire   +1 more source

Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

Communications in Mathematics and Statistics, 2017
We study a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, which is based on an analogy between the BSDE and reinforcement learning with the gradient of ...
Weinan E, Jiequn Han, Arnulf Jentzen
semanticscholar   +1 more source

Stochastic Differential Equations

2009
The chapter begins with Section 4.1 in which motivational examples of random walks and stochastic phenomena in nature are presented. In Section 4.2 the concept of random processes is introduced in a more precise way. In Section 4.3 the concept of a Gaussian and Markov random process is developed. In Section 4.4 the important special case of white noise
Alexander Kukush, Andrey Pilipenko, Dmytro Gusak, Alexey Kulik, Yuliya Mishura   +4 more
  +7 more sources

Stochastic Differential Equations and Applications

, 1998
This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form.
X. Mao
semanticscholar   +1 more source

Applied Stochastic Differential Equations

, 2019
The topic of this book is stochastic differential equations (SDEs). As their name suggests, they really are differential equations that produce a different “answer” or solution trajectory each time they are solved.
Simo Särkkä, A. Solin
semanticscholar   +1 more source