0396636 20240103203016.020131031235959.9 000331073400001 84887839253 10.1090/S0065-9266-2013-00687-9 160 s. P cav_un_epca*02543310065-92662271065 (2014)1-160 Brownian web Brownian net stochastic flow of kernels measure-valued process Howitt-Warren flow linear system random walk in random environment finite graph representation cav_un_auth*0295338 Schertzer E. FR cav_un_auth*0253274 Sun R. SG cav_un_auth*0217893 Swart Jan M. Stochastická informatika Department of Stochastic Informatics SI SI UTIA-B Department of Stochastic Informatics Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2013/SI/swart-0396636.pdf GA201/07/0237 GA ČR cav_un_auth*0228641 GA201/09/1931 GA ČR cav_un_auth*0254026 It is known that certain one-dimensional nearest-neighbor random walks in i.i.d. random space-time environments have diffusive scaling limits. Here, in the continuum limit, the random environment is represented by a `stochastic flow of kernels', which is a collection of random kernels that can be loosely interpreted as the transition probabilities of a Markov process in a random environment. The theory of stochastic flows of kernels was first developed by Le Jan and Raimond, who showed that each such flow is characterized by its n-point motions. Our work focuses on a class of stochastic flows of kernels with Brownian n-point motions which, after their inventors, will be called Howitt-Warren flows. Our main result gives a graphical construction of general Howitt-Warren flows, where the underlying random environment takes on the form of a suitably marked Brownian web. This extends earlier work of Howitt and Warren who showed that a special case, the so-called `erosion flow', can be constructed from two coupled `sticky Brownian webs'. Our construction for general Howitt-Warren flows is based on a Poisson marking procedure developed by Newman, Ravishankar and Schertzer for the Brownian web. Alternatively, ... 2015 BA 3 4 A 4a 20231122135818.4 RVO:67985556 http://hdl.handle.net/11104/0225510 MATHEMATICS 3.168 3.163 Q1 97.832 95.994 Q1* Q1* 2014 Soubory v repozitáři: swart-0396636.pdf 84887839253 SCOPUS 000331073400001 WOS cav_un_epca*0254331 Memoirs of the American Mathematical Society 0065-9266 1947-6221 Roč. 227 č. 1065 2014 1 160