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 ...
Read More
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.
Read Less
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Fine. Sewn binding. Cloth over boards. 232 p. Mathematics and Its Applications, 438. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Fine. Sewn binding. Cloth over boards. 232 p. Mathematics and Its Applications, 438. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.