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pro vyhledávání: '"Barnes, Clayton"'
Consider the $[0,1]$-valued continuous random field solution $(u_t(x))_{t\geq 0, x\in \mathbb R}$ to the one-dimensional stochastic heat equation \[ \partial_t u_t = \frac{1}{2}\Delta u_t + b(u_t) + \sqrt{u_t(1-u_t)} \dot W, \] where $b(1)\leq 0\leq
Externí odkaz:
http://arxiv.org/abs/2402.11160
Consider a system of Brownian particles on the real line where each pair of particles coalesces at a certain rate according to their intersection local time. Assume that there are infinitely many initial particles in the system. We give a necessary a
Externí odkaz:
http://arxiv.org/abs/2211.15298
Simulations support the conjecture that the dimension of the trace of Brownian earthworm is strictly greater than 3/2.
Externí odkaz:
http://arxiv.org/abs/2207.11625
We consider the $[0,1]$-valued solution $(u_{t,x}:t\geq 0, x\in \mathbb R)$ to the one dimensional stochastic reaction diffusion equation with Wright-Fisher noise \[\partial_t u= \partial_x^2 u + f(u) + \epsilon \sqrt{u(1-u)} \dot W.\] Here, $W$ is a
Externí odkaz:
http://arxiv.org/abs/2107.09377
Publikováno v:
Journal of African Foreign Affairs, 2022 Apr 01. 9(1), 31-52.
Externí odkaz:
https://www.jstor.org/stable/27159677
Autor:
Barnes, Clayton
We prove existence and uniqueness of a reaction-diffusion equation whose diffusivity is a non-linear functional of the boundary temperature. We do this by studying systems of one-dimensional reflecting diffusions whose noise is a function of the refl
Externí odkaz:
http://arxiv.org/abs/1812.01058
Akademický článek
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We construct a class of reflection laws for billiard processes in the unit interval whose stationary distribution for the billiard position and its velocity is the product of the uniform distribution and the standard normal distribution. These billia
Externí odkaz:
http://arxiv.org/abs/1811.02529
Autor:
Barnes, Clayton
Consider a random walker on the nonnegative lattice, moving in continuous time, whose positive transition intensity is proportional to the time the walker spends at the origin. In this way, the walker is a jump process with a stochastic and adapted j
Externí odkaz:
http://arxiv.org/abs/1809.04428
Autor:
Barnes, Clayton
In 2001, Knight constructed a stochastic process modeling the one dimensional interaction of two particles, one being Newtonian in the sense that it obeys Newton's laws of motion, and the other particle being Brownian. We construct a multi-particle a
Externí odkaz:
http://arxiv.org/abs/1710.06562