Zobrazeno 1 - 10
of 150
pro vyhledávání: '"Klebaner, F."'
Publikováno v:
J. Math. Biol. 88, 44 (2024)
We consider stochastic dynamics of a population which starts from a small colony on a habitat with large but limited carrying capacity. A common heuristics suggests that such population grows initially as a Galton-Watson branching process and then it
Externí odkaz:
http://arxiv.org/abs/2303.03735
Publikováno v:
Journal of Mathematical Biology 80, 1733-1757 (2020)
How long does it take for an initially advantageous mutant to establish itself in a resident population, and what does the population composition look like then? We approach these questions in the framework of the so called Bare Bones evolution model
Externí odkaz:
http://arxiv.org/abs/1902.07976
Many populations, e.g. of cells, bacteria, viruses, or replicating DNA molecules, start small, from a few individuals, and grow large into a noticeable fraction of the environmental carrying capacity $K$. Typically, the elements of the initiating, sp
Externí odkaz:
http://arxiv.org/abs/1806.03506
Publikováno v:
Adv. Appl. Probab. 50 (2018) 67-81
The effect of small noise in a smooth dynamical system is negligible on any finite time interval. Here we study situations when it persists on intervals increasing to infinity. Such asymptotic regime occurs when the system starts from initial conditi
Externí odkaz:
http://arxiv.org/abs/1802.06231
Autor:
Klebaner, F. C., Mogulskii, A. A.
We establish, under the Cramer exponential moment condition in a neighbourhood of zero, the Extended Large Deviation Principle for the Random Walk and the Compound Poisson processes in the metric space $\V$ of functions of finite variation on $[0,\in
Externí odkaz:
http://arxiv.org/abs/1610.09472
Publikováno v:
Journal of Applied Probability Vol 53(2016), No 4, 1193-1205
The paper presents a phenomenon occurring in population processes that start near zero and have large carrying capacity. By the classical result of Kurtz~(1970), such processes, normalized by the carrying capacity, converge on finite intervals to the
Externí odkaz:
http://arxiv.org/abs/1510.04819
We consider a sequence of processes defined on half-line for all non negative t. We give sufficient conditions for Large Deviation Principle (LDP) to hold in the space of continuous functions with a new metric that is more sensitive to behaviour at i
Externí odkaz:
http://arxiv.org/abs/1502.06342
Autor:
Klebaner, F., Liptser, R.
Let $\mathfrak{z}$ be a stochastic exponential, i.e., $\mathfrak{z}_t=1+\int_0^t\mathfrak{z}_{s-}dM_s$, of a local martingale $M$ with jumps $\triangle M_t>-1$. Then $\mathfrak{z}$ is a nonnegative local martingale with $\E\mathfrak{z}_t\le 1$. If $\
Externí odkaz:
http://arxiv.org/abs/1112.0430
Autor:
Chigansky, P., Klebaner, F. C.
Publikováno v:
Electronic Communications in Probability, 17 (2012), no. 29, 10 pp
We prove weak convergence of triangular arrays to the compound Poisson limit using Tikhomirov's method. The result is applied to statistical estimation of the threshold parameter in autoregressive models.
Comment: 11 pages, to appear in Electron
Comment: 11 pages, to appear in Electron
Externí odkaz:
http://arxiv.org/abs/1110.5381
The CEV model is given by the stochastic differential equation $X_t=X_0+\int_0^t\mu X_sds+\int_0^t\sigma (X^+_s)^pdW_s$, $\frac{1}{2}\le p<1$. It features a non-Lipschitz diffusion coefficient and gets absorbed at zero with a positive probability. We
Externí odkaz:
http://arxiv.org/abs/1005.0728