TY - CHAP
T1 - Stochastic Differential Equations
AU - Schuss, Zeev
N1 - Publisher Copyright:
© 2010, Springer Science+Business Media, LLC.
PY - 2010
Y1 - 2010
N2 - Dynamics driven by white noise, often written as (4.1) or is usually understood as the integral equation (4.2) where and are random coefficients, which can be interpreted in several different ways, depending on the interpretation of the stochastic integral in (4.2) as Itô, Stratonovich, backward, or otherwise. Different interpretations lead to very different solutions and to qualitative differences in the behavior of the solution. For example, a noisy dynamical system of the form (4.1) may be stable if the Itô integral is used in (4.2), but unstable if the Stratonovich or the backward integral is used instead. Different interpretations lead to different numerical schemes for the computer simulation of the equation. A different approach, based on path integrals, is given in Chapter 5.
AB - Dynamics driven by white noise, often written as (4.1) or is usually understood as the integral equation (4.2) where and are random coefficients, which can be interpreted in several different ways, depending on the interpretation of the stochastic integral in (4.2) as Itô, Stratonovich, backward, or otherwise. Different interpretations lead to very different solutions and to qualitative differences in the behavior of the solution. For example, a noisy dynamical system of the form (4.1) may be stable if the Itô integral is used in (4.2), but unstable if the Stratonovich or the backward integral is used instead. Different interpretations lead to different numerical schemes for the computer simulation of the equation. A different approach, based on path integrals, is given in Chapter 5.
KW - Brownian Motion
KW - Conditional Expectation
KW - Planck Equation
KW - Stochastic Differential Equation
KW - Uniqueness Theorem
UR - http://www.scopus.com/inward/record.url?scp=85067928584&partnerID=8YFLogxK
U2 - 10.1007/978-1-4419-1605-1_4
DO - 10.1007/978-1-4419-1605-1_4
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AN - SCOPUS:85067928584
T3 - Applied Mathematical Sciences (Switzerland)
SP - 92
EP - 132
BT - Applied Mathematical Sciences (Switzerland)
PB - Springer
ER -