Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Butkovsky, Oleg"'
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:
Butkovsky, Oleg, Gallay, Samuel
We study a multidimensional stochastic differential equation with additive noise: $$ d X_t=b(t, X_t) dt +d \xi_t, $$ where the drift $b$ is integrable in space and time, and $\xi$ is either a fractional Brownian motion or an $\alpha$-stable process.
Externí odkaz:
http://arxiv.org/abs/2311.12013
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
We study the strong rate of convergence of the Euler--Maruyama scheme for a multidimensional stochastic differential equation (SDE) $$ dX_t = b(X_t) \, dt + dL_t, $$ with irregular $\beta$-H\"older drift, $\beta > 0$, driven by a L\'evy process with
Externí odkaz:
http://arxiv.org/abs/2204.12926
Motivated by the challenges related to the calibration of financial models, we consider the problem of numerically solving a singular McKean-Vlasov equation $$ d X_t= \sigma(t,X_t) X_t \frac{\sqrt v_t}{\sqrt {E[v_t|X_t]}}dW_t, $$ where $W$ is a Brown
Externí odkaz:
http://arxiv.org/abs/2203.01160
Publikováno v:
Electron. J. Probab. 28: 1-25 (2023)
We analyze the law of the SLE tip at a fixed time in capacity parametrization. We describe it as the stationary law of a suitable diffusion process, and show that it has a density which is a unique solution of a certain PDE. Moreover, we identify the
Externí odkaz:
http://arxiv.org/abs/2110.11247
A fully discrete finite difference scheme for stochastic reaction-diffusion equations driven by a $1+1$-dimensional white noise is studied. The optimal strong rate of convergence is proved without posing any regularity assumption on the non-linear re
Externí odkaz:
http://arxiv.org/abs/2110.06148
We study stochastic reaction--diffusion equation $$ \partial_tu_t(x)=\frac12 \partial^2_{xx}u_t(x)+b(u_t(x))+\dot{W}_{t}(x), \quad t>0,\, x\in D $$ where $b$ is a generalized function in the Besov space $\mathcal{B}^\beta_{q,\infty}({\mathbb R})$, $D
Externí odkaz:
http://arxiv.org/abs/2011.13498
Autor:
Butkovsky, Oleg, Wunderlich, Fabrice
In this short note we show how the asymptotic strong Feller property (ASF) and local weak irreducibility can be established via generalized couplings. We also prove that a stronger form of ASF together with local weak irreducibility implies uniquenes
Externí odkaz:
http://arxiv.org/abs/1912.06121
Akademický článek
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