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1-20 of 29 Search Results for

#### wiener

Book Chapter

Series: AIPP Books, Professional

Published: March 2023

EISBN: 978-0-7354-2547-7

ISBN: 978-0-7354-2544-6

... in Physics: The Part of Common Sense ( Springer Science and Business Media , 2001 ). Wiener , G. , “ Elementary particle physics in early physics ,” Education , Ph.D. thesis ( University of Vienna , 2017 ). Wiener , G. J. et al. , Phys. Educ. 52 ( 4 ), 044001 ( 2017a ). 10.1088...

Book Chapter

Series: AIPP Books, Professional

Published: March 2023

10.1063/9780735425477_009

EISBN: 978-0-7354-2547-7

ISBN: 978-0-7354-2544-6

.... et al. , Environ. Behav. 18 ( 1 ), 75 – 93 ( 1986 ). 10.1177/0013916586181004 Viennot , L. , Reasoning in Physics: The Part of Common Sense ( Springer Science and Business Media , 2001 ). Wiener , G. , “ Elementary particle physics in early physics ,” Education , Ph.D...

Book

Series: AIPP Books, Professional

Published: March 2023

10.1063/9780735425477

EISBN: 978-0-7354-2547-7

ISBN: 978-0-7354-2544-6

Book Chapter

Series: AIPP Books, Principles

Published: December 2021

10.1063/9780735423718_006

EISBN: 978-0-7354-2371-8

ISBN: 978-0-7354-2368-8

...

*physical Brownian motion*. On the other hand, the mathematician sees Brownian motion as another name for the Wiener process, that is, the random variable*W*(*t*) introduced in Sec. 4.2.4, and in particular in (4.15)–(4.17), whose conditional probability density obeys the equation ∂ t...Book Chapter

Series: AIPP Books, Methods

Published: September 2022

0

EISBN: 978-0-7354-2435-7

ISBN: 978-0-7354-2432-6

... ( 1502 ), 2453 – 2464 ( 2008 ). 10.1098/rstb.2007.2230 Strong , W. , “ Biased richness and evenness relationships within Shannon–Wiener index values ,” Ecol. Indic. 67 , 703 – 713 ( 2016 ). 10.1016/j.ecolind.2016.03.043 Suter II , G. W. , Ecological Risk Assessment ( CRC...

Book Chapter

Series: AIPP Books, Methods

Published: September 2022

10.1063/9780735424357_005

EISBN: 978-0-7354-2435-7

ISBN: 978-0-7354-2432-6

.... , Domingos , T. , and Kooijman , S. , “ From empirical patterns to theory: A formal metabolic theory of life ,” Philos. Trans. R. Soc., B 363 ( 1502 ), 2453 – 2464 ( 2008 ). 10.1098/rstb.2007.2230 Strong , W. , “ Biased richness and evenness relationships within Shannon–Wiener index...

Book

Series: AIPP Books, Methods

Published: September 2022

10.1063/9780735424357

EISBN: 978-0-7354-2435-7

ISBN: 978-0-7354-2432-6

Book Chapter

Series: AIPP Books, Perspectives

Published: July 2022

10.1063/9780735424715_005

EISBN: 978-0-7354-2471-5

ISBN: 978-0-7354-2469-2

... i j d K i j d x i j , and d W ^ i j is the symmetric matrix formed by independent increments of the Wiener process

*d**W*_{ij}, (5.31) d W ^ i j = 1 2 ( d W i j + d W i...Images

**Published:**December 2021

FIG. 6.1 Conditional probability and corresponding sample paths for a Wiener process: a) Spreading of an initially sharp distribution

*p*(*w*,*t*|*w*_{0},*t*_{0}) with increasing time*t*−*t*_{0}; b) Three simulated sample paths of the Wiener process, illustrating their great variability. More about this image found in Conditional probability and corresponding sample paths for a Wiener process...Images

**Published:**December 2021

FIG. 6.3 A simulated Brownian bridge, shown in red, interpolates between a pair of points on a more coarsely simulated Wiener process. More about this image found in A simulated Brownian bridge, shown in red, interpolates between a pair of p...

Book Chapter

Series: AIPP Books, Principles

Published: December 2021

0

EISBN: 978-0-7354-2371-8

ISBN: 978-0-7354-2368-8

...References for Chapter 5 References for Chapter 5 [5.1] C. W. Gardiner , Stochastic Methods , 4 th ed. ( Springer , Heidelberg, Berlin , 2009 ). [5.2] N. Wiener ,

*Generalized harmonic analysis*, Acta Math. 55 , 117 ( 1930 ). [5.3] A. Khinchin...Book Chapter

Series: AIPP Books, Principles

Published: December 2021

10.1063/9780735423718_015

EISBN: 978-0-7354-2371-8

ISBN: 978-0-7354-2368-8

...Markov processes that are homogeneous in time and space are known as Lévy processes. The Wiener process has this property, but there is a more extensive class of such processes, which can all be described by a master equation or by a limit of a master equation. The homogeneity property means...

Book Chapter

Series: AIPP Books, Principles

Published: December 2021

10.1063/9780735423718_007

EISBN: 978-0-7354-2371-8

ISBN: 978-0-7354-2368-8

... +

*i*Δ*t*(which means that*t*_{N}≡*t*). Now note that the*Wiener increments*of Sec. 6.2.2 can be defined in terms of*ξ*(*t*) as (7.3) Δ W i ≡ ∫ t i t i + 1 ξ ( t ) d t . From the properties of*ξ*...Book

Series: AIPP Books, Principles

Published: December 2021

10.1063/9780735423718

EISBN: 978-0-7354-2371-8

ISBN: 978-0-7354-2368-8

Book Chapter

Series: AIPP Books, Principles

Published: December 2021

10.1063/9780735423718_009

EISBN: 978-0-7354-2371-8

ISBN: 978-0-7354-2368-8

... ) ) ) . The Stationary and Diffusive Cases: When

*k*= 0 the stochastic differential equation ( 9.2 ) reduces to the Wiener process, which we call the diffusive case of the Ornstein–Uhlenbeck process. This result is trivial, but in many-variable processes the concept acquires a less trivial status...Book Chapter

Series: AIPP Books, Principles

Published: December 2021

10.1063/9780735423718_008

EISBN: 978-0-7354-2371-8

ISBN: 978-0-7354-2368-8

..., show that the solution of the equation ( 8.8 ) is given by

*p*(*x*,*t*) = e^{kt}*p*(*x*e^{kt}, 0). The Wiener Process The Wiener process is a diffusion process with*A*(*x*,*t*) = 0 and*B*(*x*...Book Chapter

Series: AIPP Books, Principles

Published: December 2021

10.1063/9780735423718_005

EISBN: 978-0-7354-2371-8

ISBN: 978-0-7354-2368-8

... of fluctuations is given by The Wiener–Khinchin Theorem: The spectrum of fluctuations is only well defined when the system is stationary. The relationship between the stationary autocorrelation function

*g*_{ S }(*t*) and the spectrum is known as the Wiener–Khinchin theorem [ 5.2 , 5.3...Book Chapter

Series: AIPP Books, Principles

Published: December 2021

10.1063/9780735423718_004

EISBN: 978-0-7354-2371-8

ISBN: 978-0-7354-2368-8

... selection of points according to the conditional probability at points in time—the algorithm is given by ( 4.17 ). The path is very irregular, but continuous. Simulation Algorithm Using Wiener Increment: We get a simulation algorithm for non-constant

*B*(*x*,*t*) by evaluating...Book Chapter

Series: AIPP Books, Principles

Published: December 2021

10.1063/9780735423718_016

EISBN: 978-0-7354-2371-8

ISBN: 978-0-7354-2368-8

... a different kind of summation over Ornstein–Uhlenbeck processes, and is valid for H > 1 2 , but not for H < 1 2 . Mandelbrot’s Representation A natural representation of a stationary Gaussian process

*G*(*t*) can be expressed directly in terms of the Wiener process...Book Chapter

Series: AIPP Books, Methods

Published: December 2021

0

EISBN: 978-0-7354-2366-4

ISBN: 978-0-7354-2364-0

... Wiener , O. , “ Stehende Lichtwellen und die Schwingungsrichtung polarisirten Lichtes ,” Ann. Phys. 276 ( 6 ), 203 – 243 ( 1890 ). 10.1002/andp.18902760603 Wieser , W. , Biedermann , B. R. , Klein , T. , “ Multi-megahertz OCT: High quality 3D imaging at 20 million A-scans...

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