Zobrazeno 1 - 10
of 183
pro vyhledávání: '"Mytnik, Leonid"'
Consider the stochastic heat equation \begin{equation*} \partial_t u_t(x)=\frac12 \partial^2_{xx}u_t(x) +b(u_t(x))+\dot{W}_{t}(x),\quad t\in(0,T],\, x\in [0,1], \end{equation*} where $b$ is a generalized function, and $\dot W$ is space-time white noi
Externí odkaz:
http://arxiv.org/abs/2410.06599
Autor:
Butkovsky, Oleg, Mytnik, Leonid
We put forward a new method for proving weak uniqueness of stochastic equations with singular drifts driven by a non-Markov or infinite-dimensional noise. We apply our method to study stochastic heat equation (SHE) driven by Gaussian space-time white
Externí odkaz:
http://arxiv.org/abs/2405.13780
Autor:
Mytnik, Leonid, Weinberger, Johanna
We consider the one-dimensional stochastic differential equation \begin{equation*} X_t = x_0 + L_t + \int_0^t \mu(X_s)ds, \quad t \geq 0, \end{equation*} where $\mu$ is a finite measure of Kato class $K_{\eta}$ with $\eta \in (0,\alpha-1]$ and $(L_t)
Externí odkaz:
http://arxiv.org/abs/2404.13729
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
Autor:
Hong, Jieliang, Mytnik, Leonid
For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in Perkins (1990) that if the underlying spatial motion belongs to a certain class of L\'evy processes that admit jumps, then with probability one the closed support of $X_t$ is th
Externí odkaz:
http://arxiv.org/abs/2311.13757
We study a continuous time Mutually Catalytic Branching model on the $\mathbb{Z}^{d}$. The model describes the behavior of two different populations of particles, performing random walk on the lattice in the presence of branching, that is, each parti
Externí odkaz:
http://arxiv.org/abs/2310.17497
We consider stochastic differential equation $$ d X_t=b(X_t) dt +d W_t^H, $$ where the drift $b$ is either a measure or an integrable function, and $W^H$ is a $d$-dimensional fractional Brownian motion with Hurst parameter $H\in(0,1)$, $d\in\mathbb{N
Externí odkaz:
http://arxiv.org/abs/2302.11937
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
Autor:
Glöde, Patric Karl, Mytnik, Leonid
We study the longtime behavior of a continuous state Symbiotic Branching Model (SBM). SBM can be seen as a unified model generalizing the Stepping Stone Model, Mutually Catalytic Branching Processes, and the Parabolic Anderson Model. It was introduce
Externí odkaz:
http://arxiv.org/abs/2209.09323