In
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
, the Skorokhod problem is the problem of solving a
stochastic differential equation with a reflecting boundary condition.
The problem is named after
Anatoliy Skorokhod who first published the solution to a stochastic differential equation for a
reflecting Brownian motion
In probability theory, reflected Brownian motion (or regulated Brownian motion, both with the acronym RBM) is a Wiener process in a space with reflecting boundaries. In the physical literature, this process describes diffusion in a confined space ...
.
Problem statement
The classic version of the problem states
that given a
càdlàg process and an
M-matrix ''R'', then stochastic processes and are said to solve the Skorokhod problem if for all non-negative ''t'' values,
# ''W''(''t'') = ''X''(''t'') + ''R Z''(''t'') ≥ 0
# ''Z''(0) = 0 and d''Z''(''t'') ≥ 0
#
.
The matrix ''R'' is often known as the reflection matrix, ''W''(''t'') as the reflected process and ''Z''(''t'') as the regulator process.
See also
List of things named after Anatoliy Skorokhod {{Short description, none
These are things named after Anatoliy Skorokhod (1930-2011), a Ukrainian mathematician.
Skorokhod
* Skorokhod space
* Skorokhod integral
* Skorokhod problem
Skorokhod's
* Skorokhod's theorem:
** Skorokhod's embeddi ...
References
Stochastic calculus
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