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pro vyhledávání: '"Kurtz, Thomas G."'
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial position and l
Externí odkaz:
http://arxiv.org/abs/2305.14488
Autor:
Costantini, Cristina, Kurtz, Thomas G.
Publikováno v:
Stochastic Process. Appl. 170 (2024) 104295
We prove existence and uniqueness for semimartingale reflecting diffusions in 2-dimensional piecewise smooth domains with varying, oblique directions of reflection on each "side", under geometric, easily verifiable conditions. Our conditions are opti
Externí odkaz:
http://arxiv.org/abs/2206.05621
Autor:
Costantini, Cristina, Kurtz, Thomas G.
Publikováno v:
The Annals of Applied Probability, 2024, Vol. 34, No. 4, 3665-3700
Bass and Pardoux (1987) deduce from the Krein-Rutman theorem a reverse ergodic theorem for a sub-probability transition function, which turns out to be a key tool in proving uniqueness of reflecting Brownian Motion in cones in Kwon and Williams (1991
Externí odkaz:
http://arxiv.org/abs/2106.07208
Autor:
Costantini, Cristina, Kurtz, Thomas G.
Publikováno v:
In Stochastic Processes and their Applications April 2024 170
We introduce a weighted particle representation for the solution of the filtering problem based on a suitably chosen variation of the classical de Finetti theorem. This representation has important theoretical and numerical applications. In this pape
Externí odkaz:
http://arxiv.org/abs/2104.04773
Autor:
Kurtz, Thomas G., Swanson, Jason
We consider a diffusion given by a small noise perturbation of a dynamical system driven by a potential function with a finite number of local minima. The classical results of Freidlin and Wentzell show that the time this diffusion spends in the doma
Externí odkaz:
http://arxiv.org/abs/2101.07290
Autor:
Kurtz, Thomas G., Swanson, Jason
We consider a diffusion given by a small noise perturbation of a dynamical system driven by a potential function with a finite number of local minima. The classical results of Freidlin and Wentzell show that the time this diffusion spends in the doma
Externí odkaz:
http://arxiv.org/abs/1906.03212
Autor:
Costantini, Cristina, Kurtz, Thomas G.
Publikováno v:
Electron. J. Probab. 24 (2019), no. 135
Constrained Markov processes, such as reflecting diffusions, behave as an unconstrained process in the interior of a domain but upon reaching the boundary are controlled in some way so that they do not leave the closure of the domain. In this paper,
Externí odkaz:
http://arxiv.org/abs/1901.10770
Akademický článek
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Autor:
Costantini, Cristina, Kurtz, Thomas G.
Publikováno v:
Electron. J. Probab. 23 (2018), no. 84
We consider stochastic differential equations with (oblique) reflection in a $2$-dimensional domain that has a cusp at the origin, i..e. in a neighborhood of the origin has the form $\{(x_1,x_2):0
Externí odkaz:
http://arxiv.org/abs/1710.06281