Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
612-822-4611

  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Random Fields and Stochastic Partial Differential Equations

Random Fields and Stochastic Partial Differential Equations

Rozanov, Y.

Hardcover

Series: Mathematics and Its Applications, Book 438

General MathematicsProbability & Statistics

ISBN10: 0792349849
ISBN13: 9780792349846
Publisher: Springer Nature
Published: Mar 31 1998
Pages: 232
Weight: 1.14
Height: 0.56 Width: 6.14 Depth: 9.21
Language: English
This book considers some models described by means of partial dif- ferential equations and boundary conditions with chaotic stochastic disturbance. In a framework of stochastic Partial Differential Equa- tions an approach is suggested to generalize solutions of stochastic Boundary Problems. The main topic concerns probabilistic aspects with applications to well-known Random Fields models which are representative for the corresponding stochastic Sobolev spaces. {The term stochastic in general indicates involvement of appropriate random elements. ) It assumes certain knowledge in general Analysis and Probability {Hilbert space methods, Schwartz distributions, Fourier transform) . I A very general description of the main problems considered can be given as follows. Suppose, we are considering a random field in a region T Rd which is associated with a chaotic (stochastic) source' by means of the differential equation (*) in T. A typical chaotic source can be represented by an appropri- ate random field' with independent values, i. e., generalized random function' = ( cp, 'TJ), cp E C (T), with independent random variables ( cp, 'fJ) for any test functions cp with disjoint supports. The property of having independent values implies a certain roughness of the ran- dom field ' which can only be treated functionally as a very irregular Schwarz distribution. With the lack of a proper development of non- linear analyses for generalized functions, let us limit ourselves to the 1 For related material see, for example, J. L. Lions, E.

1 different editions

Also available

Also in

General Mathematics

View All