Zobrazeno 1 - 10
of 187
pro vyhledávání: '"Parviainen, Mikko"'
We establish Krylov-Safonov type H\"older regularity theory for solutions to quite general discrete dynamic programming equations or equivalently discrete stochastic processes on random geometric graphs. Such graphs arise for example from data clouds
Externí odkaz:
http://arxiv.org/abs/2410.01642
We study a general class of parabolic equations $$ u_t-|Du|^\gamma\big(\Delta u+(p-2) \Delta_\infty^N u\big)=0, $$ which can be highly degenerate or singular. This class contains as special cases the standard parabolic $p$-Laplace equation and the no
Externí odkaz:
http://arxiv.org/abs/2404.06161
We study sequential cost-efficient design in a situation where each update of covariates involves a fixed time cost typically considerable compared to a single measurement time. The problem arises from parameter estimation in switching measurements o
Externí odkaz:
http://arxiv.org/abs/2403.02245
We study a general form of a degenerate or singular parabolic equation $$ u_t-|Du|^{\gamma}\big(\Delta u+(p-2)\Delta_\infty^Nu\big)=0 $$ that generalizes both the standard parabolic $p$-Laplace equation and the normalized version that arises from sto
Externí odkaz:
http://arxiv.org/abs/2304.00108
We introduce a notion of convexity with respect to a one-dimensional operator and with this notion find a one-parameter family of different convexities that interpolates between classical convexity and quasiconvexity. We show that, for this interpola
Externí odkaz:
http://arxiv.org/abs/2301.10573
Autor:
Arroyo, Ángel, Parviainen, Mikko
We propose a new version of the tug-of-war game and a corresponding dynamic programming principle related to the $p$-Laplacian with $1
Externí odkaz:
http://arxiv.org/abs/2212.10807
Autor:
Parviainen, Mikko
The objective is the interplay between stochastic processes and partial differential equations. To be more precise, we focus on the connection between the nonlinear p-Laplace equation, and the stochastic game called tug-of-war with noise. The connect
Externí odkaz:
http://arxiv.org/abs/2208.09732
We obtain an analytic proof for asymptotic H\"older estimate and Harnack's inequality for solutions to a discrete dynamic programming equation. The results also generalize to functions satisfying Pucci-type inequalities for discrete extremal operator
Externí odkaz:
http://arxiv.org/abs/2207.01655
In this paper we prove an asymptotic $C^{1,\gamma}$-estimate for value functions of stochastic processes related to uniformly elliptic dynamic programming principles. As an application, this allows us to pass to the limit with a discrete gradient and
Externí odkaz:
http://arxiv.org/abs/2206.09001
Publikováno v:
Bull. London Math. Soc., 55 (2023): 470-489
We prove an elliptic Harnack's inequality for a general form of a parabolic equation that generalizes both the standard parabolic $p$-Laplace equation and the normalized version that has been proposed in stochastic game theory. This version of the in
Externí odkaz:
http://arxiv.org/abs/2202.02350