Zobrazeno 1 - 10
of 194
pro vyhledávání: '"Bass, Richard F."'
Autor:
Bass, Richard F., Burdzy, Krzysztof
Consider the Skorokhod problem in the closed non-negative orthant: find a solution $(g(t),m(t))$ to \[ g(t)= f(t)+ Rm(t),\] where $f$ is a given continuous vector-valued function with $f(0)$ in the orthant, $R$ is a given $d\times d$ matrix with 1's
Externí odkaz:
http://arxiv.org/abs/2407.05140
Autor:
Bass, Richard F., Burdzy, Krzysztof
Consider the Skorokhod equation in the closed first quadrant: \[ X_t=x_0+ B_t+\int_0^t{\bf v}(X_s)\, dL_s,\] where $B_t$ is standard 2-dimensional Brownian motion, $X_t$ takes values in the quadrant for all $t$, and $L_t$ is a process that starts at
Externí odkaz:
http://arxiv.org/abs/2405.06144
Autor:
Bass, Richard F., Burdzy, Krzysztof
For $f: [0,1]\to \mathbb R$, we consider $L^f_t$, the local time of space-time Brownian motion on the curve $f$. Let ${\cal S}_\alpha$ be the class of all functions whose H\"older norm of order $\alpha$ is less than or equal to 1. We show that the su
Externí odkaz:
http://arxiv.org/abs/2307.13001
Autor:
Bass, Richard F.
Let $\{L^z_t\}$ be the jointly continuous local times of a one-dimensional Brownian motion and let $L^*_t=\sup_{z\in \mathbb R} L^z_t$. Let $V_t$ be any point $z$ such that $L^z_t=L^*_t$, a most visited site of Brownian motion. We prove that if $\gam
Externí odkaz:
http://arxiv.org/abs/1303.2040
Autor:
Bass, Richard F.
We consider a degenerate stochastic differential equation that has a sticky point in the Markov process sense. We prove that weak existence and weak uniqueness hold, but that pathwise uniqueness does not hold nor does a strong solution exist.
Externí odkaz:
http://arxiv.org/abs/1210.1075
Autor:
Bass, Richard F., Gordina, Maria
We consider the Harnack inequality for harmonic functions with respect to three types of infinite dimensional operators. For the infinite dimensional Laplacian, we show no Harnack inequality is possible. We also show that the Harnack inequality fails
Externí odkaz:
http://arxiv.org/abs/1209.1573
Autor:
Bass, Richard F., Ren, Hua
Let $\alpha\in (0,2)$, let $${\cal E}(u,u)=\int_{\Bbb R^d}\int_{\Bbb R^d} (u(y)-u(x))^2\frac{A(x,y)}{|x-y|^{d+\alpha}}\, dy\, dx$$ be the Dirichlet form for a stable-like operator, let $$\Gamma u(x)=\int_{\Bbb R^d} (u(y)-u(x))^2\frac{A(x,y)}{|x-y|^{d
Externí odkaz:
http://arxiv.org/abs/1207.2715