{"product_id":"numerical-integration-of-stochastic-differential-equations-von-g-n-milstein","title":"Numerical Integration of Stochastic Differential Equations","description":"\u003cp\u003eU sing stochastic differential equations we can successfully model systems that func­ tion in the presence of random perturbations. Such systems are among the basic objects of modern control theory. However, the very importance acquired by stochas­ tic differential equations lies, to a large extent, in the strong connections they have with the equations of mathematical physics. It is well known that problems in math­ ematical physics involve 'damned dimensions', of ten leading to severe difficulties in solving boundary value problems. A way out is provided by stochastic equations, the solutions of which of ten come about as characteristics. In its simplest form, the method of characteristics is as follows. Consider a system of n ordinary differential equations dX = a(X) dt. (O.l ) Let Xx(t) be the solution of this system satisfying the initial condition Xx(O) = x. For an arbitrary continuously differentiable function u(x) we then have: (0.2) u(Xx(t)) - u(x) = j (a(Xx(t)), ~~ (Xx(t))) dt.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9780792332138\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9789048144877\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Hardcover - 9780792332138","offer_id":50827073478,"sku":"9780792332138","price":149.79,"currency_code":"EUR","in_stock":true},{"title":"Softcover - 9789048144877","offer_id":39415514660957,"sku":"9789048144877","price":149.79,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/bc722a8d-6495-40b5-bc12-7e7f839b77d0.jpg?v=1772176795","url":"https:\/\/shop.autorenwelt.de\/en\/products\/numerical-integration-of-stochastic-differential-equations-von-g-n-milstein","provider":"Autorenwelt Shop","version":"1.0","type":"link"}