1.0Arbeitsgemeinschaft der Universitätsverlagehttps://universitaetsverlage.euXMLRPChttps://universitaetsverlage.eu/author/xmlrpc/rich600338<blockquote class="wp-embedded-content"><a href="https://universitaetsverlage.eu/bucher-e-books/titel/variational-integrators-and-generating-functions-for-stochastic-hamiltonian-systems/">Variational integrators and generating functions for stochastic Hamiltonian systems</a></blockquote> <script type='text/javascript'> <!--//--><![CDATA[//><!-- /*! This file is auto-generated */ !function(d,l){"use strict";var e=!1,o=!1;if(l.querySelector)if(d.addEventListener)e=!0;if(d.wp=d.wp||{},!d.wp.receiveEmbedMessage)if(d.wp.receiveEmbedMessage=function(e){var t=e.data;if(t)if(t.secret||t.message||t.value)if(!/[^a-zA-Z0-9]/.test(t.secret)){var r,a,i,s,n,o=l.querySelectorAll('iframe[data-secret="'+t.secret+'"]'),c=l.querySelectorAll('blockquote[data-secret="'+t.secret+'"]');for(r=0;r<c.length;r++)c[r].style.display="none";for(r=0;r<o.length;r++)if(a=o[r],e.source===a.contentWindow){if(a.removeAttribute("style"),"height"===t.message){if(1e3<(i=parseInt(t.value,10)))i=1e3;else if(~~i<200)i=200;a.height=i}if("link"===t.message)if(s=l.createElement("a"),n=l.createElement("a"),s.href=a.getAttribute("src"),n.href=t.value,n.host===s.host)if(l.activeElement===a)d.top.location.href=t.value}}},e)d.addEventListener("message",d.wp.receiveEmbedMessage,!1),l.addEventListener("DOMContentLoaded",t,!1),d.addEventListener("load",t,!1);function t(){if(!o){o=!0;var e,t,r,a,i=-1!==navigator.appVersion.indexOf("MSIE 10"),s=!!navigator.userAgent.match(/Trident.*rv:11\./),n=l.querySelectorAll("iframe.wp-embedded-content");for(t=0;t<n.length;t++){if(!(r=n[t]).getAttribute("data-secret"))a=Math.random().toString(36).substr(2,10),r.src+="#?secret="+a,r.setAttribute("data-secret",a);if(i||s)(e=r.cloneNode(!0)).removeAttribute("security"),r.parentNode.replaceChild(e,r)}}}}(window,document); //--><!]]> </script><iframe sandbox="allow-scripts" security="restricted" src="https://universitaetsverlage.eu/bucher-e-books/titel/variational-integrators-and-generating-functions-for-stochastic-hamiltonian-systems/embed/" width="600" height="338" title="„Variational integrators and generating functions for stochastic Hamiltonian systems“ — Arbeitsgemeinschaft der Universitätsverlage" frameborder="0" marginwidth="0" marginheight="0" scrolling="no" class="wp-embedded-content"></iframe>https://universitaetsverlage.eu/wp-content/uploads/asolmerce/image-9783866441552.jpg452640In this work, the stochastic version of the variational principle is established, important for stochastic symplectic integration, and for structure-preserving algorithms of stochastic dynamical systems. Based on it, the stochastic variational integrators in formulation of stochastic Lagrangian functions are proposed, and some applications to symplectic integrations are given. Three types of generating functions in the cases of one and two noises are discussed for constructing new schemes.