My research area is
"stochastic processes and their applications".
The theory of stochastic
processes is, within mathematics, part of probability theory. I am
particularly interested in interacting particle systems, interacting
diffusions, superprocesses, kombinatorial stochastic processes, fractal
geometry and path properties of measure-valued diffusions, as well as
applications of the theory of stochastic processes in mathematical
genetics, mathematical population biology and statistical physics.
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Mein Fachgebiet ist
"Stochastische Prozesse und deren Anwendungen".
Die Theorie stochastischer
Prozesse gehoert innerhalb der Mathematik zur
Wahrscheinlichkeitstheorie. Speziell interessieren mich komplexe
interagierende Partikelsysteme, interagierende Diffusionen,
Superprozesse, kombinatorische stochastische Prozesse, fraktale
Geometrie und Pfadeigenschaften von masswertigen Diffusionen, sowie die
Anwendung der Theorie stochastischer Prozesse in der mathematischen
Genetik, der mathematischen Populationsbiologie sowie der statistischen
Physik.
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Below, please find some focal areas of my research, together with
selected corresponding publications.
- Path- and fractal properties of measure-valued diffusions
and Gaussian processes:
- Blath, J.; Moerters, P.: Thick points of super-Brownian
motion. Probab. Theory Related Fields
131, no. 4, 604-630, (2005)
- Blath, J.: Martin, A.: Propagation of singularities in
the
semi-fractional Brownian sheet, Stochastic
Process.
Appl.
118, no. 7, 1264-1277, (2008)
- Blath, J.: Measure-valued Processes, Self-Similarity,
and
Flickering Random Measures, Fractal Geometry and Stochastics IV, Birkhaeuser Progress in Probability, Vol.
61,
175-196,
(2009)
- Birkner, M.; Blath, J.: Rescaled stable generalised
Fleming-Viot processes: Flickering random measures, Electron. J. Probab. 14, 2418-2437,
(2009)
- Stochastic partial differential equations, interacting
diffusions and mathematical population dynamics
- Blath, J; Doering, L; Etheridge, A.: On the moments and
the
interface of the symbiotic branching model, Annals of Probability 39, 252-290,
(2011)
- Blath, J.; Etheridge, A.; Meredith, M.: Coexistence in
locally regulated competing populations and survival of branching
annihilating random walk, Ann. Appl.
Probab. 17, nos. 5/6, 1474-1507,
(2007)
- Mathematical genetics, genealogies and related inference
problems
- Birkner, M.; Blath, J., Steinruecken, M.: Importance
Sampling for Lambda Coalescents in the infinitely many sites model, Theor. Pop. Biology, 33 pages, in
press, (2011)
- Birkner, M.; Blath, J., Moehle, M.; Steinruecken, M.;
Tams,
J.: A modified lookdown construction for the Xi-Fleming-Viot process
with mutation and populations with recurrent bottlenecks, ALEA Lat. Am. J. Probab. Math. Stat. 6,
25--61
(2009)
- Birkner, M.; Blath, J.: Measure-valued diffusions,
general
coalescents and population genetic inference, Trends in Stochastic Analysis, LMS 353,
Cambridge
University
Press, 329-363, (2009)
- Birkner, M.; Blath, J.: Computing likelihoods for
coalescents with multiple collisions in the infinitely-many-sites
model, J. Math. Biology 57,
no.
3, 435-465, (2008)
- Birkner, M.; Blath, J., Steinruecken, M.: Analysis of
DNA
sequence variation within marine species using Beta-coalescents, TUB
preprint, 13 pages, (2011)
- Branching processes and coalescent processes
- Birkner, M.; Blath, J.; Capaldo, M.; Etheridge, A.;
Moehle,
M.; Schweinsberg, J.; Wakolbinger, A.: Alpha-stable branching and
Beta-coalescents. Electron. J.
Probab. 10, Paper no. 9, 303-325, (2005)
- Birkner, M.; Blath, J., Moehle, M.; Steinruecken, M.;
Tams,
J.: A modified lookdown construction for the Xi-Fleming-Viot process
with mutation and populations with recurrent bottlenecks, ALEA Lat. Am. J. Probab. Math. Stat. 6,
25--61
(2009)
- Branching-annihilating particle systems
- Blath, J.; Kurt, N.: On Survival and Extinction of
Caring
Double-Branching Annihilating Random Walk, to appear in Electron. Comm. Probab., 12 pages,
(2011)
- Blath, J.; Etheridge, A.; Meredith, M.: Coexistence in
locally regulated competing populations and survival of branching
annihilating random walk, Ann. Appl.
Probab. 17, nos. 5/6, 1474-1507,
(2007)
Last modified: 26 April 2011.
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